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ORIGINAL PAPER 

Application of ANN in the prediction of the pore

concentration of aluminum metal foams manufactured

by powder metallurgy methods

Sermin Ozan & Mustafa Taskin & Sedat Kolukisa &

Mehmet Sirac Ozerdem

Received: 20 March 2007 /Accepted: 22 August 2007 /Published online: 22 September 2007# Springer-Verlag London Limited 2007

Abstract In this work, the effect of fabrication parameters

on the pore concentration of aluminum metal foam,manufactured by the powder metallurgy process, has been

studied. The artificial neural network (ANN) technique has

 been used to predict pore concentration as a function of 

some key fabrication parameters. Aluminum metal foam

specimens were fabricated from a mixture of aluminum

 powders (mean particle size 60 μ m) and NaCl at 10, 20, 30,

40(wt)% content under a pressure of 200, 250, and

300 MPa. All specimens were then sintered at 630°C for 

2.5 h in argon atmosphere. For pore formation (foaming),

sintered specimens were immersed into 70°C hot running

water. Finally, the pore concentration of specimens was

recorded to analyze the effect of fabrication parameters

(namely, NaCl ratio, NaCl particle size, and compacting

 pressure) on the foaming behavior of compacted specimens. It 

has been recorded that the above-mentioned fabrication

 parameters are effective on pore concentration profile while

 pore diameters remain unchanged. In the ANN training

module, NaCl content (wt)%, NaCl particle size (μ m), and

compacting pressure (MPA) were employed as inputs, while

 pore concentration % (volume) of compacts related to

fabrication parameters was employed as output. The ANN program was successfully used to predict the pore concentra-

tion % (volume) of compacts related to fabrication parameters.

Keywords Aluminum metal foam . Pore concentration .

Fabrication parameters . Neural network 

1 Introduction

Cellular metallic materials have attracted more and more

attention in the last few decades with increased availability

of practical manufacturing technologies and improved

understanding of their physical, chemical, and mechanical

 propert ies [1 – 4]. Aluminum (Al) foams have found

increasing applications in a wide range of structural and

functional products due to their exceptional mechanical,

thermal, acoustic, electrical, and chemical properties [5, 6].

Aluminum foam structures have densities only fractions of 

that of a solid structure and therefore have high specific

strength and stiffness. They also have excellent properties

for impact energy, vibration, and sound absorption. Examples

of their applications include lightweight panels for building

and transport designed to resist buckling and impact, and

nonflammable ceiling and wall panels for thermal and sound

insulation. There is a great diversity of cellular metallic

materials that show various structures and properties. Accord-

ing to the connectivity of cells, cellular metals can be

categorized as either closed or open-celled. Open cell foams

can also be used as heat exchangers, filters, and catalyst 

carriers. Applications of Al foams on a large scale are likely to

enter the automotive industry with an aim to improve vehicle

crashworthiness and thus passenger safety. Closed-cell Al

foams are also materials of increasing importance because of 

Int J Adv Manuf Technol (2008) 39:251 – 256

DOI 10.1007/s00170-007-1218-2

S. Ozan : M. Taskin (*)

Faculty of Technical Education, University of Firat,

23119 Elazig, Turkey

e-mail: mtaskin@firat.edu.tr 

S. Ozan

e-mail: serozan@firat.edu.tr 

S. Kolukisa : M. S. Ozerdem

Faculty of Engineering and Architecture, University of Dicle,

21280 Diyarbakir, Turkey

S. Kolukisa

e-mail: kolukisa@dicle.edu.tr 

M. S. Ozerdem

e-mail: sozerdem@dicle.edu.tr 

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their energy absorption capabilities combined with good

thermal and acoustic properties.

Manufacturing methods [7, 8] currently available can be

generally grouped into five categories according to the

forms of the precursory Al and the types of the pore-

forming agents, namely, melt-gas injection, melt-foaming

agent, powder-foaming agent, investment casting, and melt 

infiltration. However, the Al foams produced by these

methods are either too expensive due to the high productioncosts or too poor in quality due to poor controllability in

 pore structure and porosity. As a consequence, commercial

applications of Al foam components are still limited. With

the rapidly increasing demand for high quality Al foams,

there has been a growing need for developing cost effective

manufacturing technologies. With the developments in

artificial intelligence, researchers have paid a great deal of 

attention to the solution of nonlinear problems in physical

and mechanical properties [9]. Electricity demand forecast-

ing, prediction of mechanical and physical properties of 

alloys, composite materials as a function of components,

and fabrication parameters are all application areas of ANN.

The aim of this paper is to predict the pore concentration %

(volume) of Al –  NaCl compacts manufactured by powder 

metallurgy using ANN. Features of a multilayer perceptron

architecture with a back-propagation learning algorithm [10]

were employed to predict the pore concentration % (volume)

of aluminum foam as a function of fabrication parameters.

2 Experimental data collection

The Al –  NaCl powders were mixed at a prespecified weight 

ratio. The resultant Al –  NaCl powder mixture is compacted

into a net-shape preform under a pressure of 200, 250, or 

300 MPa. The preform is then sintered at 630°C for 2.5 h in

argon atmosphere below the melting point of Al (660°C) and

far below that of NaCl (801°C). After the aluminum in the

 preform forms a well-bonded networked structure, the

 preform is cooled to room temperature. The embedded NaCl

 particles are finally dissolved in hot water, leaving behind an

open cell aluminum metal foam with the same chemical

composition as that of the original aluminum powder. For 

Fig. 1 Optical micrographs of aluminum metal foam cross sections

F ig . 2 Sintering – dissolution

 process (SDP) consists of the

mixing, compacting, sintering

and dissolution stages

252 Int J Adv Manuf Technol (2008) 39:251 – 256

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each combination, three samples were fabricated and mean

values were recorded for foaming evaluations. Optical micro-

graphs of aluminum metal foam cross sections are given in

Fig. 1. The sintering – dissolution process (SDP) consists of 

the mixing, compacting, sintering, and dissolution stages as

shown schematically in Fig. 2. SEM micrographs of 

compacts (S1-S2) are presented in Fig. 3. Pore concentration

(volume) values of compacts related to fabrication parame-

ters were presented in Table 1.

3 Artificial neural network (ANN) model

An ANN is a mathematical model consisting of a number 

of highly interconnected processing elements organized

into layers, the geometry and functionality of which have

 been likened to that of the human brain. ANNs learn by

experience, generalizing from previous experiences to new

ones, and can make decisions [11].

The network has one input layer, one hidden layer, and

one output layer. The input layer consists of all the input 

factors. Information from the input layer is then processed

in the course of one hidden layer, then the output vector iscomputed in the final (output) layer. A schematic descrip-

tion of the layers is given in Fig. 4. In developing an ANN

model, the available data set is divided into two sets, one is

to be used for training of the network, and the remaining is

to be used to verify the generalization capability of the

network. Input  – output pairs are presented to the network 

and weights are adjusted to minimize the error between the

network output and actual value.

Among the various kinds of ANN approaches that exist,

the multi layer perceptron (MLP) architecture with the back-

 propagation learning algorithm has become the most popular 

in engineering applications [12]. The back-propagationalgorithm, which is common in literature, has been used

to update the forward path parameters in ANNs. This

method is based on minimization of the quadratic cost 

function by tuning the network parameters. The mean

square error is considered a measurement criterion for a

training set. Parameters which minimize this cost function

are determined. The averaged square error is given in

Eqs. 1 and 2 such that:

e j  nð Þ ¼ d  j  nð Þ À y j  nð Þ ð1Þ

" nð Þ ¼1

2 P 

X j 2C 

X P 

n¼1

e2 j  nð Þ ð2Þ

Here e, n, d, y, P , and C  indicate error signal at the output,

iteration number, desired output, generated output by

network, total number of patterns contained in the training

Fig. 3 SEM micrographs of compacts (S1-S2) samples

Table 1 Pore concentration % (volume) of compacts related to

fabrication parameters

Sample

 No:

 NaCl

content (wt) %

 NaCl

 particlesize (μ m)

Compacting

 pressure(MPA)

Pore

concentration %(volume)

S1- 10 500 200 7.00

S1a 10 1,100 200 7.20

S1b 10 500 250 6.00

S1c 10 1,100 250 6.60

S1d 10 500 300 5.40

S1e 10 1,100 300 6.10

S2- 20 500 200 14.60

S2a 20 1,100 200 15.30

S2b 20 500 250 13.40

S2c 20 1,100 250 14.20

S2d 20 500 300 13.00

S2e 20 1,100 300 14.80

S3- 30 500 200 27.00S3a 30 1,100 200 28.60

S3b 30 500 250 24.70

S3c 30 1,100 250 26.30

S3d 30 500 300 24.80

S3e 30 1,100 300 26.10

S4- 40 500 200 37.00

S4a 40 1,100 200 38.60

S4b 40 500 250 34.70

S4c 40 1,100 250 36.30

S4d 40 500 300 34.90

S4e 40 1,100 300 36.10Fig. 4 Structure of three layered neural network in the present study

Int J Adv Manuf Technol (2008) 39:251 – 256 253

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set, and number of neurons at the output layer, respectively.

The adjustment of synaptic weights between the hidden layer 

and the output layer can be found from Eqs. 3 and 4:

Δw ji nð Þ ¼ hd  j  nð Þ yi nð Þ ð3Þ

δ  j  nð Þ ¼ e j  nð Þφ 0Xm

i¼0

w ji nð Þ yi nð Þ

!ð4Þ

Where 8 ′ indicates a derivative of the activation

function. The adjustment of synaptic weight coefficients

 between input layer and hidden layer are given in Eq. 5:

δ  j  nð Þ ¼ 8 0 X

m

i¼0

w ji nð Þ yi nð Þ !Xk 

δ k  nð Þwkj  nð Þ ð5Þ

where η  indicates learning rate parameters and has different 

values for different problems. In the case in which the

network does not converge, a formula, which is used to

determine weight coefficients including the α momentum

 parameter, has been generalized [11] and given as Eq. 6:

Δw ji nð Þ ¼ a Δw ji n À 1ð Þ þ hd  j  nð Þ yi nð Þ ð6ÞThe general architecture of learning and predicting the

mechanical properties system is given in Fig. 5.

The MATLAB platform was used to train and test the ANN.

In the training, an increased number of neurons (5 – 12) in the

hidden layer has been used in order to define the output 

accurately. After training the network successfully, it was

tested by using the known data. Statistical methods were

used to compare the results produced by the network. Errors

occurring at the learning and testing stages are called the root 

mean squared (RMS), absolute fraction of variance (R 2), and

mean percentage error (MPE) values.

4 Results and discussion

Pore concentration (pore volume per total structure volume)

is a function of NaCl ratio, NaCl particle size, and

Fig. 5 General architecture of 

the learning and predicting

system

Fig. 6 Performance changing of neural network in the training stage

Table 2 MLP architecture and training parameters

 Number of layers 3

 Number of neurons on the layers Input: 3, hidden: 8,

output: 1

Initial weights and biases Randomly between−

1and +1

Activation functions for hidden and

output layers

Log-sigmoid

Training parameters learning rule Back-propagation

Adaptive learning rate for hidden layer 0.9

Adaptive learning rate for output layer 0.7

 Number of iterations 365

Momentum constant 0.95

Duration of learning time 4.026 s

Acceptable mean-squared error 0.001

254 Int J Adv Manuf Technol (2008) 39:251 – 256

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compacting pressure of the powder metallurgy process

while sintering temperature and time are kept unchanged.

 NaCl content has significant effects on foaming behavior 

especially at high NaCl content as shown in Table 1. At 

small rate additions (10%) of NaCl, pore percent is nearly

6%. This can be explained by the existence of closed cells

resulting in retained NaCl in the structure. The amount of 

retained NaCl decreased at higher NaCl contents.

 NaCl particle size slightly affects the foaming behavior,

and larger particle size resulted in higher pore concen-

trations of the specimens. Finally, from test results it has

 been recorded that the compacting pressure is effective on

foaming behavior and higher pressure reduced the pore

concentration of specimens.

An ANN model was employed to predict the pore

concentration % (volume) of aluminum foam as a function

of fabrication parameters. The network has three input 

 parameters: NaCl content (wt) %, NaCl particle size (μ m),

and compacting pressure (MPA) and one output parameter,

namely, pore concentration. Thus, the architecture of the

ANN model becomes 3-8-1, such that, 3 corresponds to the

input values, 8 to the number of hidden layer neurons, and

1 to the output.

The experimental data set includes 24 patterns, of which

16 patterns were used for training the network and 8 were

selected randomly to test the performance of the trained

network. All the input and output values were normalized

 between 0.1 and 0.9 by using linear scaling. The log-

sigmoid transfer function was used in the hidden and output 

layer. During the training period, the averaged square error 

decreased with increasing number of iterations. After 365

training cycles, a significant effect on error reduction has

not been traced. The performance changing of ANN in the

training stage is given in Fig. 6.

As is evident from Fig. 6, an increasing number of 

reliable input data improves the integrity of the training

session and target outputs. The MLP architecture and

training parameters used in the learning stage for the

ANN structure are presented in Table 2. A comparison of 

Fig. 7 Comparison of training and testing stage of pore concentration

Fig. 8 a Scatter plot for training stage. b Scatter plot for testing stage

Table 3 Weights between input layer and hidden layer 

Ei=G1* NaCl content + G2* NaCl particle size + G3* compacting

 pressure + G4

i G1 G2 G3 G4

1 −0.15272 −0.38902 −0.61348 −0.81661

2 −2.6374 −0.17147 0.48371 1.8031

3−

1.6536−

0.66814−

0.14308 0.67409

4 2.7159 −0.57562 0.15041 −0.72595

5 −0.63876 −0.25752 0.90339 0.31034

6 0.92124 0.85744 0.13134 −0.0192

7 −1.3023 0.50668 0.62245 −0.33923

8 −0.6561 −0.4741 −0.81 −0.33923

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the measured and predicted pore concentrations at training

and testing stages is presented in Fig. 7. From thesecomparison charts, it can be clearly seen that the ANN is

 properly trained and showed a consistency among the

 parameters.

The verification results by ANN are shown in Fig. 8a,b

as scatterplots. It can be seen from the scatter diagrams that 

the slope and intercept of the regression equations for the

outputs are significantly close to 1 and 0, respectively. The

scatterplots reveal that the well-trained network model has

great accuracy in predicting the pore concentration of 

fabricated aluminum foam.

The decision of the number of neurons used in the

hidden layer usually depends on the arithmetical mean of the number of inputs and outputs. In this application, 5 – 12

hidden layers were employed to test. The algorithm with

eight hidden layer neurons is used in the present applica-

tion. Weights between input layer and hidden layer,

 produced for the present output, namely, pore concentra-

tion, are presented in Table 3.

The activation function used in this study is given as

follows:

 M i ¼1

1 þ eÀ E ið7Þ

where E i is the weighted sum of the input depending on the bonding period and process temperature. The constants for 

calculation of  M i were taken from Table 3.

The outputs are calculated as follows:

Pore concentration ¼

1.

1þeÀ À0:53 M 1À3:3 M 2À1:78 M 3þ3:3 M 4À0:38 M 5þ1:49 M 6À0:84 M 7À0:55 M 8þ0:24ð Þ Statistical values of pore concentration % (volume) are

 presented in Table 4. The statistical values, namely, RMS,

R 2, and MPE, are within acceptable ranges which meet the

integrity of the ANN learning and testing stages.

5 Conclusions

Fabrication parameters, namely, NaCl particle size, NaCl

content (wt), and compacting pressure, showed significant 

effects on foaming behavior of aluminum metal foam

manufactured by the powder metallurgy process. Higher 

 particle size and ratio of NaCl increases the foaming

 behavior resulting in a higher pore concentration profile

while compacting pressure decreases the pore concentration

within given conditions, namely, at 630°C sintering

temperature for 2.5 h in argon atmosphere.The main quality indicator of a neural network is its

generalization ability, i.e., its ability to predict accurately

the output of unseen test data. In this study, we have

 benefited from these features of ANN. It has been

demonstrated that MLP architecture with the back-propa-

gation learning algorithm can be successfully used as a tool

for predicting the pore concentration % (volume) of 

aluminum foams as a function of fabrication parameters.

This method could be also employed in predicting other 

 properties of engineering materials based on experimental

studies.

Acknowledgement The authors are grateful to the Dicle University

Research Committee since this work is suggested and supported

through grant DUAPAK 03-MF-86. Special thanks to TUBITAK (The

Scientific and Technological Research Council of Turkey) for their 

unfailing support to the researchers.

References

1. Banhart J, Ashby MF, Fleck NA (1999) Metal foams and porous

metal structures. MIT-Verlag, Bremen, Germany

2. Gibson LJ, Ashby MF (1988) Cellular solids: structures and

 properties. Pergamon Press, Oxford, pp 132

3. Davies GJ, Zhen S (1983) Review: metallic foams: their 

 production, properties and applications. J Mater Sci 18:1899 – 

1911

4. Seitzberger M, Rammerstorfer FG, Degischer HP, Gradinger R 

(1997) Crushing of axially compressed steel tubes filled with

aluminum foam. Acta Mech 125:93 – 105

5. Shapovalov VI (1993) Method for manufacturing porous articles.

US Patent 5,181,549, 26 January 1993

6. Yu C-J, Banhart J (1997) Mechanical properties of metallic foams.

Fraunhofer USA metal foam symposium, 7 – 8 October, J. Banhart 

ve H. Eifert, Stanton, Delaware, USA, pp 37 – 48

7. Wood JT (1997) Production and applications of continuously cast,

foamed aluminum. Fraunhofer USA metal foam symposium,

7 – 8 October, J. Banhart ve H. Eifert, Stanton, Delaware, USA,

 pp 31 – 

358. Zhao CY, Lu TJ, Hodson HP (2004) Thermal radiation in

ultralight metal foams with open cells. Int J Heat Mass Trans 47

(14):2927 – 2939

9. Hsiang S, Kuo J (2005) Applying ANN to predict the forming

load and mechanical property of magnesium alloy under hot 

extrusion. IJAMT 26:970 – 977

10. Haykin S (1994) Neural networks, a comprehensive foundation.

McMillian College, New York, pp 198 – 203

11. Kohonen T (1980) Content addressable memories. Springer,

Berlin Heidelberg New York, pp 168 – 172

12. Tandon V, El-Mounayri H (2001) A novel artificial neural

networks force model for end milling. IJAMT 18:693 – 700

Table 4 Statistical values of pore concentration % (volume)

RMS train R2 train MPE train RMS test R2 test MPE test  

Pore concentration 1.86258 0.996073 2.90827 1.83976 0.995682 1.54519

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