ORIGINAL ARTICLE

Design of an optimized procedure to predict oppositeperformances in porthole die extrusion

G. Ambrogio • F. Gagliardi

Received: 9 September 2011 / Accepted: 16 March 2012 / Published online: 1 April 2012

� Springer-Verlag London Limited 2012

Abstract The main objective of advanced manufacturing

control techniques is to provide efficient and accurate tools

in order to control the set-up of machines and manufac-

turing systems. Recent developments and implementations

of expert systems and neural networks support this aim.

This research explores the combined use of neural net-

works and Taguchi’s method to enhance the performance

of porthole die extrusion process; the energy saving and the

quality of the welding line are two conflicting objectives of

the process taken into account. The complexity of the

analysis, due to the number of the involved variables, does

not allow the representation of the specified outputs by

means of a simple analytical approach. The implementa-

tion of a more accurate and sophisticated tool, such as the

neural network, results more efficient and easier to be

integrated into a simple ‘‘ready to use’’ procedure for

predicting the investigated outputs. The main limit to wider

implementation of neural networks is the huge computation

resources (times and capacities) required to build the data

set; a finite element approach was adopted to overcome the

time and money wasting typical of experimental investi-

gations. Satisfactory results in terms of prediction capa-

bility of the highlighted outputs were found. Finally, a

simple and integrated interface was designed to make

easier the application of the proposed procedure and to

allow the generalization to other manufacturing processes.

Keywords Extrusion � Porthole � ANN � DoE � Taguchi

1 Introduction

In a competitive marketplace, good quality and low cost

manufacturing products are, of course, one of the most

sought-after goals. Firstly, the customer agrees to pay if he

recognizes higher characteristics in the product, such as

better mechanical properties or increasing performance; at

the same time, the producers need to find better operating

conditions, which ensure reduction of industrial costs [1].

These aims can rarely be found in a single solution; more

often the production choices represent a compromise

between the customer requests and lower industrial costs.

Due to this compromise, manufacturing processes need to

be closely monitored and designed to ensure the quality

standards and to choose the process conditions, which

ensure the possible lower costs. Beyond the particular

manufacturing process taken into account, there is a great

need for an automatic and effective methodology, which

can indicate its making state. Artificial neural networks

(ANNs) can be used for this purpose due to their ability to

imitate the human brain [2]. This technique is suited for

problems that involve the manipulation of multiple

parameters and nonlinear interpolation [3]. Starting by the

same base of knowledge, the ANNs allow to simulta-

neously evaluate more than a single output of the process.

These tools find applicability in several fields of science

including engineering, medicine, agriculture. The auto-

motive factories can be, for example, used like a case of

study; these factories belong to the manufacturing sector,

which typically presents several complexities to solve.

From this point of view, Lolas and Olatumbosun [4]

demonstrated how a neural network architecture could

G. Ambrogio (&) � F. Gagliardi

Department of Mechanical Engineering,

University of Calabria, 87036 Rende, CS, Italy

e-mail: g.ambrogio@unical.it

URL: http://tsl.unical.it

F. Gagliardi

e-mail: f.gagliardi@unical.it

123

Neural Comput & Applic (2013) 23:195–206

DOI 10.1007/s00521-012-0916-3

predict the reliability performance of a vehicle at later

stages of its life; same assumptions can be extended to each

item used to realize the car. For example, the polymer

composites are often utilized in the automotive industry,

and the neural network approach can be used to predict the

mechanical properties of these materials [5].

The neural network (NN) approach is obviously appli-

cable to the manufacturing processes too [6]. The manu-

facturing scenario and the material design represent some

of the most promising and natural application fields for this

kind of methodology; due to the intrinsic complexity that

characterizes these contests, the neural networks result

widely utilized in the last years as predictive tool [7–9].

Moreover, Dae-Cheol et al. [10] suggested a method of

preform design in a multistage metal forming processes

based on ANN; they also proposed the workability forecast

limited by ductile fracture.

Lucignano et al. [11] implemented two NNs to optimize

the aluminium extrusion process determining the temper-

ature profile of an AA6060 alloy in two different equip-

ment zones. A conclusion of this study was that the

temperature profiles, predicted by the neural network,

closely agree with experimental values. Previously, Suk-

thomya and Tannock [12] compared methods for training

NNs to analyse complex manufacturing processes; they

provided some interesting guidelines and highlighted the

real implementation in industry by using a case study.

In this paper, the porthole die extrusion was considered

and the prediction of the process performances at varying

of all the geometrical and technological variables was

taken into account by means of an ANN. The extrusion by

porthole die is one of the most used manufacturing pro-

cesses to produce hollow components; its feasibility is

directly dependent by the availability of a complex die

structure, which allows to obtain the desired shape. A lot of

factors involved in the process with effects that conflict on

the measured outputs. Therefore, the process design is

quite difficult due to the geometrical parameters that need

to be set-up, such us the bridge shape, the width of the

bridge and the height of the welding chamber. Actually, the

problem is that these parameters are derived only after few

trial and error experiments; vice versa, the availability of a

tool that helps the designer during the preliminary set-up

definition could make easier the process applicability and

reduce the start-up time. A pure analytical approach results

unsuitable due to the large number of variables to take into

account and the nonlinearity of the phenomenon to analyse;

none of the finite element analysis (FEA) is competitive

due to some drawbacks that penalize its use, such as the

high computational time and the remeshing problem [13].

The approach proposed in this paper is based on the use

of an optimized artificial neural network that, starting from

a given process condition, supplies an effective and fast

prediction of two output variables: (1) the maximum load

required to carry out the process and (2) the quality of the

welding line. In a reliable range, by an inverse approach,

the process designer can, easily, find the better configura-

tion to execute the process reducing the load and increasing

the quality of the extruded part. The described procedure

has given satisfactory results for a set of investigated cases,

as accurately discussed in the following sections.

2 Optimized procedure for neural network design

From an industrial point of view and for any type of pro-

cess, the prediction capability of suitable output perfor-

mance is considered strategic for everyone [14]. The

proposed methodology tries to satisfy this need in a more

efficient and effective way reducing time and resources.

The approach is based on the combined use of the NN, as

highly performance predictive tool [15, 16], and the Design

of Experiments (DoE), to reduce the test number and to

ensure the robustness of the analysis [17].

As it is well known, multilayer feed-forward networks

(commonly referred as multilayer perceptrons) are an

important class of NNs. Multilayer perceptrons networks

suggested by Rumelhart et al. [18] have been successfully

applied to solve some difficult and diverse problems in

many disciplines of science and technology, when non-

linear solution is required. The procedure normally

involves training of the network in a supervised or unsu-

pervised manner. The network typically consists of a set of

sensory units (source nodes) that constitute the input layer,

one or more hidden layer of computation nodes and an

output layer of computation nodes. The input signal

propagates through the networks in a forward direction in a

layer-by-layer basis. The data for teaching the artificial

neural network need to be carefully selected, and a wide

range of data, more than those to be found, should be

trained. As a consequence, there is the necessity to have an

adequate quantity of experimental data available since the

NN predictive capability is related to the data set dimen-

sion: higher is the number of the training data set, higher is

the NN predictive capability to generalize. In the manu-

facturing field, the number of experimental data for the NN

design cannot be easily increased being largely time- and

resource consuming; at the same time, a careful NN design

results time-consuming due to the number of NN mor-

phologies to test. Due to these aspects, a simple search for

the optimal NN does not supply additional information in

matter of factor significance, nor it guarantees the result

quality. To overcome these drawbacks, an optimized pro-

cedure, based on the hybrid approach of both finite element

method (FEM) and DoE, was proposed in the following

study. First of all, the FEM allowed to improve the

196 Neural Comput & Applic (2013) 23:195–206

123

knowledge of the process itself and to acquire more

information on the process mechanics. In general, to

decrease development times, it is necessary to apply finite

element analysis (FEA) even in the very first step of a

design process, since it serves the opportunity for a sig-

nificant speed-up of the design process. However, when the

simulation process results to be too much complex, model

simplification has to be taken into account, like in this

study.

Contemporarily, the statistical DoE is used to get

information such as main effects and their interaction,

starting from the minimum number of experiments or, in

this case, the minimum number of NN run. The design

objective in the statistical DoE is to find a good combi-

nation of controllable factors. The Taguchi’s method,

which is one of the fractional designs, has a good repre-

sentation of experiment concerning only the main effects of

the design parameters including noise factors [19]. The

Taguchi’s DoE allows to highlight the main factors that

have to be considered into the investigation, and to verify

the quality of the analysed networks starting from the

evaluation of some performance indexes. Contemporarily,

it drives the designer in the selection of the NN parameter

set-up, which minimizes the network sensitivity from an

external noise [20].

The proposed procedure tries to address this issue fol-

lowing the below-discussed steps (Fig. 1):

1. Key process variables and constrain identification:

Each manufacturing process is characterized by a set

of variables, both numerical and categorical. To build

a predictive tool, it is necessary to well understand

which possible input variables really affect the desired

outputs; a preliminary step is focalized on a better

definition of the problem, involved factors and possible

bonds.

2. Data collection: In general, both the experimental

investigation in the laboratory and the numerical

model can be applied to build the data set.

3. Efficient search for the optimal NN configuration by

means of the statistical analysis: The DoE was used to

determine the NN, which ensures better prediction of.

4. Toolbox design: Implementation of a simple and

‘‘ready to use’’ procedure in order to predict the

process output.

While the first two steps are strongly related to the

considered problem, the optimal NN identification can be

formalized into a more general way. As concern the third

phase, a careful NN design requires first of all a pre-

liminary phase that establishes the analysis perimeter; this

is necessary to determine all the possible network config-

urations and the algorithms that have to be considered and

tested. At the same time, the choice and the number of

parameters that have to be taken into account affect the

design performance. The methodology proposed is based

on a more formal approach derived by the Taguchi’s DoE

[19–21]. The Taguchi’s method drives the designer in the

selection of an optimal network multilayer perceptron

(MLP), which well describes the connection between input

and output factors and minimizes the network sensitivity to

an external noise. This is possible through the analysis of

variance (ANOVA) and the analysis of means (ANOM);

the ANOVA establishes the relative significance of factors

Fig. 1 Implemented procedure

for a robust process control

Neural Comput & Applic (2013) 23:195–206 197

123

in terms of their percentage contribution to the response,

while the ANOM estimates the main effects of each factor.

The ANOVA is also necessary for estimating the error

variance for the effects and variance of the prediction error

[22]. The analysis is performed on signal-to-noise ratio

(S/N ratio) to obtain the contribution of each factor.

A break point into the analysis is the choice of the

learning algorithm; several studies identify in the error

back propagation (EBP) a good solution [23–25]. The main

idea of the EBP is that the errors propagate backwards from

the output nodes to the inner nodes. During each training

iteration, the gradient of the error of the network is mea-

sured and used in a simple stochastic gradient descent

algorithm to find weights that minimize the error. In this

paper, the Levemberg-Marquardt (LM) algorithm was

applied because it gives better results, especially during the

training phase [26]. Specifically, the LM is also based on

the back-propagation approach, but it allows to overcome

the loss of convergence, which typically affects the EBP

[11, 27]. Actually, the LM algorithm is a blend of the

gradient descendent and Gaussian-Newton iteration, since

these methods are complementary in the advantages they

provide; the parameter updating in the gradient descendent

approach is performed by adding the negative of the scaled

gradient at each step, that is,

xiþ1 ¼ xi � krf ð1Þ

where xi is the parameter value at the actual step, rf is the

gradient of a nonlinear least square function f(x) and k is a

factor used to influence the gradient descent.

Levenberg and Marquardt instead proposed an algo-

rithm whose update rule is given as

xiþ1 ¼ xi � ðH þ kdiag½H�Þ�1rf ðxiÞ ð2Þ

where H and rf are the Hessian matrix and the gradient

evaluated at xi, respectively, and k is a factor that increases

or decreases to influence the descent. If the error goes down

following an update, it implies that quadratic assumption

on f(x) is working, and in this way, the factor k can be

reduced (usually by a factor of 10) to decrease the influence

of gradient descent. If the error goes up, k is increased by

the same factor, to follow the gradient more. Since the

Hessian is proportional to the curvature of f (x), the Eq. (2)

implies a large step in the direction with low curvature (i.e.

an almost flat terrain) and a small step in the direction with

high curvature (i.e. a steep incline).

According to this theoretical aspect, the LM algorithm is

in no way optimal but is just a heuristic and it works

extremely well in practice [11]. The only flaw is its need

for matrix inversion as part of the update. Even though the

inverse is usually implemented by using clever pseudo-

inverse methods such as singular value decomposition, the

cost of the update becomes prohibitive after the model size

increases to a few thousand parameters. For models of a

few hundred parameters, this method is much faster than

gradient descent; as a consequence, it was introduced to

solve problem in manufacturing scenario where the avail-

able data are generally poor [28].

Finally, considering the LM as a learning algorithm for

the NN training, the k factor is expressed by two parame-

ters: (1) the damping factor (Mu) and (2) the boost/drop

factor (Bdf); they influence the convergence velocity as

explained. While the learning algorithm was univocally

determined, the experimentation for the optimal NN search

was based on the variation of its intrinsic parameters.

Furthermore, according to the state of the art, other two

factors were utilized to generate the investigation plane for

the network design: the number of the hidden layer (NHL)

and the number of the neurons in the hidden layer (NNHL).

Different studies also highlighted the significance of this

factors and the necessity to include them into the analysis

[29, 30]. The NNHL increases the amount of connections

and weights to be fitted. This number cannot be increased

without limit because it is possible to reach a situation

where the number of connections to be fitted is larger than

the number of data pairs available for training [3]. Some

heuristics allow to find a lower and an upper bound for the

NNHLs [23]. These approaches prescribe the better way to

fix the number of neurons into the next hidden layers

dependent on the number of the input (NIN) and the output

(NON) neurons, properly decreased or increased according

to a constant. Three heuristics reported in Table 1 have

been considered in the analysis.

Finally, the range of the utilized experimental plane is

shown in Table 2, which determines 27 network configu-

rations that have to be tested, according to the Taguchi’s

theory of the orthogonal array [19]. In fact, let k = 4 be the

number of considered parameters, a not-optimized inves-

tigation leads to analyse a fully factorial plane (conven-

tional trials and errors approach), which corresponds to 3k

NN configurations at least. Instead, a fractional factorial

plane, corresponding to only 27 network configurations,

was enough according to the Taguchi’s method to reduce

the computational time for training and testing. According

to that, the time required for the optimal NN search is

reduced up to the 70 %.

Moreover, the conventional trials and error approach do

not supply additional information to the designer in matter

of factors significance, nor it guarantees a good quality of

Table 1 Used heuristics to determine the NNHLs

Lippmann (LIP) NON 9 (NIN ? 1)

Kolmogorov (KOL) 2NIN ? 1

Her Majesty’s Department of Trade and

Industry (MTI)

(NIN ? NON)/2

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the results determining very high performance cost; as a

consequence, the analysis could result incomplete. The

Taguchi’s Design of Experiments (TDoE) allows both to

highlight the main factors to be considered into the

investigation phase and to verify the quality of the inves-

tigated NNs starting from the evaluation of some perfor-

mance indexes (i.e. ANOVA, Normal Probability Plot).

The solution results more robust, and the performance costs

low [19].

3 Porthole die extrusion

The extrusion by porthole die is a process that is always

more used in order to produce hollow components; parts

with different sections can be obtained.

The process takes place through the complex die

structure composed of container, porthole, mandrel, weld-

ing chamber and bearing part (Fig. 2); the working

sequence consists of three stages that can be identified like

dividing, welding and forming stage.

The mandrel legs divide the material before that it flows

inside the welding chamber, where due to simultaneous

action of temperature and pressure, it joins again forming

welding lines [31]. Solid joining mechanics occur during

their formation similar, for instance, to the friction stir

welding [32]; two typologies of welding lines, especially,

can be found on the extruded parts, namely longitudinal

and transverse lines [33]. In order to manufacture hollow

components with better quality, understanding of mandrel

deflection and metal flow through porthole, welding

chamber and die bearing is of great importance [34]. Dif-

ferent researches have been carried out to highlight the

influences that process parameters have on the metal flow

inside the die, extrusion load and so on [35, 36].

3.1 Numerical model

The complexity of the equipment construction generates

great difficulties to carry out pure experimental investiga-

tions; the developed studies were founded, even, on FEM

analyses aimed to highlight strain, strain rate and stress

distributions in the whole porthole die. Its geometry is just

one of the variables that strongly affects the effectiveness

of the extruded part; the extrusion ratio, the porthole

number, the extrusion speed, the billet and die temperature

are further variables to be considered for the improvement

of the worked part quality [31]. However, numerical sim-

ulation presents some drawbacks, too; the analysis requires

a 3D simulation, and due to the process complexity, the

necessary computational time is high. The metal flow

inside the welding chamber is characterized by large sur-

face generation with very heavy numerical simulations.

Moreover, the strong reduction in area deeply impacts on

the remeshing–rezoning code capability, and this becomes

a possible reason of result inaccuracy. Significant mesh

distortion occurs inside the porthole die; consequently, the

simulation convergence can be reached, step by step,

through a tidier mesh obtained by numerical interpolation

from the old to the new discretization. Simplified experi-

ments and numerical model were proposed [13, 37], which

represent a good compromise between the robustness of the

analysis and the lower simulation time. They have to be

designed in order to physically reproduce the actual pro-

cess mechanics allowing, in the meantime, simpler and

quicker numerical simulations. The 2D simulations of

Table 2 Investigated factors and levels

Factors Levels

Number of hidden layers (NHL) 1

2

3

Number of hidden neurons (NHN) LIP

KOL

MTI

Damping factor (Mu) 0.001

0.05

0.25

Boost/drop factor 10

20

40

Bearing

Chamber

Mandrel

Welding

Porthole

Container

Fig. 2 Sketch of a traditional equipment for porthole die extrusion

Neural Comput & Applic (2013) 23:195–206 199

123

porthole die extrusion were especially set considering the

section reported in Fig. 3. A section plane is utilized: it cuts

the bridge of the mandrel along its axis and the welding

chamber in the zone where the two material flows weld.

The effectiveness of the welding algorithm can be tested

through 2D numerical analyses [31] with plane strain

geometry.

Despite this simplification, the porthole die extrusion

keeps high complexity. Some process and geometric vari-

ables have to be taken into account during this study: the

punch velocity (V), the die width (B), the bridge width

(BW), the bearing length (BL) and the height of the

welding chamber (HWC) were investigated. Moreover, the

bridge shape was changed too; its upper (U) and lower

(L) part were considered with both right (90�) and sharp

(45�) angles. All the investigated ranges are reported in

Table 3.

The strength of welding lines is a fundamental variable

that has to be taken into account for judging the process

goodness [32]; in literature, several criteria were intro-

duced to quantitatively evaluate this characteristic [13, 37,

38]. In this paper, the welding criterion (Q) proposed by

Plata and Piwnik [39] was taken into account; the criterion

formulation is based on the integral on time of contact

pressure (P), normalized on the actual effective stress (r),

along a generic path for a welding element according to:

Q ¼Z

t

P

rdt�C; ð3Þ

where C is the critical limit for the material welding,

function of material and process conditions. However,

higher is the value that it is possible to reach during the

extrusion, in the welding chamber, and better should be the

mechanical characteristics of the joint. This criterion was

implemented in the commercial finite element code,

DEFORM 2DTM [40] by using a customized user-

subroutine.

A second output was monitored during the numerical

campaign; this is the punch load whose value goodness

changes in antithesis with the Q value. Higher Q is usually

obtained in conjunction with higher punch load, which

instead has to be lower possible in order to reduce the die

wear, the required capacity of the press and, as conse-

quence, the energy.

The simulations were carried out modelling, as billet

material, an AA1050 whose plastic behaviour was derived

from the FE code library; the die and the punch were

modelled as rigid bodies in order to reduce the simulation

time. Mechanical analyses were executed, and the material

temperature was set equal to 500 �C. The simulations were

2D SectionSection Plane

Fig. 3 2D section extracted by a real porthole die equipment

Table 3 The process and geometric variables taken into account for

the analyses

V (mm/s) B (mm) U–L (�) BW (mm) LB (mm) HWC (mm)

1 100 45–45 12 0.5 20

90–45 3

5 130 90–90 18 6 40

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set by using an irregular initial mesh with 4500 Deform 2D

standard elements; several mesh boxes were introduced in

order to thicken the billet discretization close to the die

fillets and, in the zone of the welding chamber, where the

flows of the two material join (Fig. 4); the die and the

punch, instead, were considered rigid bodies in order to

reduce the simulation time. Adhesion between die and

deforming material was assumed; in detail, the constant

shear model was used with the frictional stress defined as:

s = mk, where s is the frictional stress, k is the shear yield

stress and m is the friction factor [40]. When there is

adhesion between material and die, the factor m is set equal

to 1. The shear stresses are probably overestimated at low

values of contact pressure; however, this condition was

carefully tested and validated [41, 42].

Naturally, the goodness of the utilized model was

already highlighted in previous research carried out by the

authors [13]: in fact, it was shown that despite the intro-

duced simplification, the 2D model allows to qualitatively

analyse the investigated variables (load and quality of the

welding line), with satisfactory results. In particular, the

comparison between experimental and numerical loads

highlighted similar trends, from a qualitative point of view

[13].

According to that, 144 numerical simulations by using

two-dimensional analyses were executed according to a

full orthogonal plane. The computational time can be found

in few hours for each simulation using a PC-Dual- Xeon

2,8 GHz with 4-GB RAM. This information has to be

highlighted considering that 3D investigations need days to

complete the numerical calculations.

Fig. 4 A numerical simulation

a at its beginning and b when

the material totally fill the

welding chamber

Table 4 The complete experiment settings

NHL NHN Mu Bdf

1 1 KOL 0.001 10

2 1 LIP 0.050 20

3 1 MTI 0.250 40

4 2 KOL 0.050 20

5 2 LIP 0.250 40

6 2 MTI 0.001 10

7 3 KOL 0.250 40

8 3 LIP 0.001 10

9 3 MTI 0.050 20

10 1 KOL 0.050 40

11 1 LIP 0.250 10

12 1 MTI 0.001 20

13 2 KOL 0.250 10

14 2 LIP 0.001 20

15 3 MTI 0.050 40

16 3 KOL 0.001 20

17 3 LIP 0.050 40

18 3 MTI 0.250 10

19 1 KOL 0.250 20

20 1 LIP 0.001 40

21 1 MTI 0.050 10

22 2 KOL 0.001 40

23 2 LIP 0.050 10

24 2 MTI 0.250 20

25 3 KOL 0.050 10

26 3 LIP 0.250 20

27 3 MTI 0.001 40

Neural Comput & Applic (2013) 23:195–206 201

123

4 Discussion of the results

The NN-Tool provided by Matlab [43] was properly

implemented to train and test the NN; the DoE analysis was

executed by using Minitab. It is well known that during a

training phase, to avoid an overfitting, it is recommended to

use a validation set for measuring the value of the error

function during the learning. The NN is then fixed when the

error value is minimum (early stopping method). This

approach requires a large data set [44]; however, in such

manufacturing process, like the one here investigated, it is

not easy to build a large data set due to the time and

resources required to make the experiments or to run a

numerical simulation. Specifically, taking into account the

porthole die extrusion, the experimental investigation

requires further energy consumption and material waste

[45], while the numerical simulation needs several hours to

converge [13]. To solve this problem, without sacrificing

the robustness of the analysis and the NN generalization

capability, Maren et al. [23] proposed to split the original

data set in training and test set.

The min–max normalization was used to transform the

original real data set. The hidden layer neurons have sig-

moidal transfer functions, and the output neuron uses a

linear activation function. Two stopping criteria were

adopted, that is sufficient accuracy and the maximum

number of iterations (the first activated). For checking the

signal of noise, a threefold cross-validation was used: the

data set was randomly split into different training set and

test set for three times. More specifically, 2/3 of the whole

data set was used as training set and the remaining 1/3 as

test set [23]. All the NNs were trained by using the con-

sidered learning algorithms and tested on each set. In this

way, starting from 27 network configurations, the whole

experimentation required the execution of 162 tests. The

complete experimental plane was synthesized in Table 4.

Finally, according to Taguchi’s method, the ANOVA

was executed to identify which factors strongly influence

the output and, as a consequence, which factors maxi-

mize the S/N ratio (i.e. minimizing the prediction error

network).

From the results of ANOVA, it was possible to identify

two control factors: the number of hidden layer (NHL) and

the number of neurons in the hidden layer (NNHL) are

highly significant for the NN performance. The factors of

the Levemberg-Marquardt’s algorithm are less significant

for the NN foresight capability. Similarly, the interaction

between NHL and NNHL is also significant; this result can

be justified taking into account the specific heuristics

implemented in the analysis to determine the NNHL [46].

Table 5 presents the results of ANOVA.

The ANOM outcomes for the investigated case can be

derived by the response diagrams as shown in Fig. 5.

Table 5 Analysis of variance for SN ratios

Source DF F P-value

NHL 2 68.72 \0.001

NHN 2 63.51 \0.001

Mu 2 2.51 0.161

BdF 2 1.30 0.340

NHL 9 NHN 4 47.44 \0.001

NHL 9 MU 4 2.76 0.128

NHL 9 BdF 4 0.49 0.747

Fig. 5 Response diagram of

S/N ratio

202 Neural Comput & Applic (2013) 23:195–206

123

The level of a factor with the highest S/N ratio is the

optimal one. According to that, the better configuration was

detected for the pattern {LIP – 1 – 0.05 – 40}, which

corresponds to the NN morphology 6-14-2 trained by set-

ting Mu = 0.05 and BdF = 40. Starting by this result, the

NN capability for predicting new data was tested and a

prediction error Y = 4.64 % was found.

Aimed at testing the generalization capability of the

network, it was decided to generate a new set of examples;

this set does not belong to any combination of input pro-

vided to the network during training and validation phase.

It was possible to test the network performance with

respect to unknown data and, at the same time, to compare

the output from the proposed network with the real one

associated with the combination of the provided input. Ten

new examples, numerically derived and characterized by

new combinations of geometric and process parameters,

were proposed to the network (see Table 6); these patterns

were not used in previous steps allowing to understand the

optimal NN generalization capability.

The NN prediction capability is graphically highlighted

in Fig. 6 with respect to the actual process load, Fmax (a),

and the welding line quality, Q (b).

According to these outcomes, a mean error prediction

equal to Y = 7.16 % was measured confirming again both

the suitability of the analysis and the possibility to apply

the NN for controlling the main process outputs.

5 Interface design between neural network

and manufacturing process

The lack of knowledge on artificial intelligent tools usually

represents a significant limitation to their use. A ‘‘user

friendly’’ toolbox (named Advanced Manufacturing Con-

trol Toolbox, AMCT) was introduced to overcome this

problem and also to complete the general procedure dis-

played in Fig. 1.

This automatic toolbox was designed by implementing a

Java code, compiled in Eclipse, and by integrating it to the

standard NN toolbox in Matlab, by means of proper user-

subroutine. The Taguchi method, instead, is not integrated

in the toolbox and needs to be managed by Minitab.

Some customized windows of the designed tool are

displayed in Fig. 7.

For a general study, the proposed procedure can be

implemented by using the same toolbox sequentially, as

shown in Fig. 8. Firstly, a problem needs to be defined, in

terms of number of input, output and data by choosing the

Generate option in the main menu. The optimal NN search

can be carried out directly through this simple interface,

avoiding the knowledge of the Matlab toolbox and by using

the Simulation option (Step 1). The results of the optimal

NN search are stored in an Excel file, which can be used in

the statistical step (Step 2). After that, the optimal NN

Table 6 Ten novel cases

Test # 1 2 3 4 5 6 7 8 9 10

V (mm/s) 5 1 1 3 5 2 2 1 5 1

B (mm) 100 130 100 90 100 100 130 90 90 100

U–L 45�–45� 90�–90� 45�–45� 45�–90� 45�–45� 90�–90� 45�–90� 45�–45� 90�–90� 45�–90�BW (mm) 18 18 18 15 15 15 12 12 12 15

LB (mm) 6 3 3 0.5 0.5 6 3 2 6 2

HWC (mm) 40 20 20 30 40 10 30 30 20 30

(a)

(b)

10000

15000

20000

25000

1 2 3 4 5 6 7 8 9 10

Loa

d [N

]

Test Number

Fmax

Fmax_pred

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

1 2 3 4 5 6 7 8 9 10

Q [

-]

Test Number

Q

Q_pred

Fig. 6 Prediction capability of the optimal NN with respect to new

data

Neural Comput & Applic (2013) 23:195–206 203

123

needs to be trained, through the Optimised NN Design

option, and properly saved (Step 3). At that point, the

optimal NN can be used automatically as a predictive tool

for the problem being investigated (Step 4).

The Advanced Manufacturing Control Toolbox is easy

to use, even if the user is not aware of all the artificial

intelligence techniques and particularly the neural network

tools.

Fig. 7 Toolbox interfaces for data prediction

Fig. 8 Advanced manufacturing control toolbox steps

204 Neural Comput & Applic (2013) 23:195–206

123

6 Conclusion

Nowadays, it is a common point of view that the avail-

ability of such predictive tools, easy to be implemented and

used, is a point of strength for a widespread application of

new and more complex production alternative. When the

trial and error investigation results particularly time-con-

suming, the coupled use of FEM analysis and optimization

method can help to improve the process knowledge and/or

to perform the design phase. In this study, the specified

techniques were invoked, and a simple and more general

procedure was firstly developed and then applied to the

porthole die extrusion. More deeply, a decision maker can

predict the main process performances of the considered

process by using the designed tool; a very fast response can

be obtained avoiding expensive trial and error experimen-

tation. Moreover, to simplify the application of the pro-

posed procedure and especially the optimal NN search, a

‘‘user friendly’’ technique was developed and tested for the

investigated problem. Finally, the toolbox can be easily

used to measure the performances of manufacturing

processes.

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