E. MALEKI, A. ZABIHOLLAH: MODELING OF SHOT-PEENING EFFECTS ON THE SURFACE PROPERTIES ...
851–860
MODELING OF SHOT-PEENING EFFECTS ON THE SURFACE
PROPERTIES OF A (TiB + TiC)/Ti–6Al–4V COMPOSITE
EMPLOYING ARTIFICIAL NEURAL NETWORKS
MODELIRANJE VPLIVA HLADNEGA POVR[INSKEGA KOVANJA
NA LASTNOSTI POVR[INE (TiB + TiC)/Ti-6Al-4V KOMPOZITA S
POMO^JO UMETNIH NEVRONSKIH MRE@
Erfan Maleki, Abolghassem Zabihollah
Sharif University of Technology, International Campus, Department of Mechanical Engineering, Kish Island,
7941776655, Iran
maleki_erfan@kish.sharif.edu, maleky.erfan@gmail.com
Prejem rokopisa – received: 2015-06-29; sprejem za objavo – accepted for publication: 2015-11-13
doi:10.17222/mit.2015.140
Titanium matrix composites (TMCs) have wide application prospects in the field of aerospace, automobile and other industries
because of their good properties, such as high specific strength, good ductility, and excellent fatigue properties. However, in
order to improve their fatigue strength and life, crack initiation and growth at the surface layers must be suppressed using
surface treatments. Shot peening (SP) is an effective surface mechanical treatment method widely used in industry which can
improve the mechanical properties of a surface. However, artificial neural networks (ANNs) have been used as an efficient
approach to predict and optimize the science and engineering problems. In the present study the effects of SP on TMC were
modeled by means of ANN and the capability of the ANN in predicting the output parameters is investigated. A back-pro-
pagation (BP) error algorithm is developed for the network training. Data of experimental tests on the (TiB + TiC)/Ti–6Al–4V
composite are employed in order to train the network. The volume fractions of the reinforcements (TiB + TiC) were 5 % and
8 %. ANN testing is accomplished using different experimental data thaat were not used during the network training. The
distance from the surface (depth) and SP intensity are regarded as input parameters and residual stress and hardness of the
Ti–6Al–4V before and after the SP and adding reinforcements are gathered as the output parameters of the network.
A comparison was made between experimental and predicted data. The predicted results were in good agreement with experi-
mental ones, which indicates that developed neural network can be used for modeling the SP process on TMCs.
Keywords: titanium matrix composites, surface treatment, shot peening, artificial neural networks, residual stress, hardness
Kompoziti na osnovi titana (TMCs) imajo {iroko mo`nost uporabe na podro~ju letalstva, avtomobilske in druge industrije zaradi
njihovih dobrih lastnosti, kot so: velika specifi~na trdnost, dobra duktilnost in odli~na odpornost na utrujanje. Vseeno pa je za
pove~anje odpornosti na utrujanje in `ivljenjsko dobo, potrebna povr{inska obdelava, da se zavre nastanek razpok in njihova rast
na povr{ini. Hladno povr{insko kovanje (SP) je u~inkovita mehanska metoda, ki se v industriji pogosto uporablja za izbolj{anje
mehanskih lastnosti povr{ine. Umetne nevronske mre`e (ANNs) se uporabljajo kot u~inkovit pribli`ek za napovedovanje in
optimiranje znanstvenih osnov in in`eniringa tega problema. V {tudiji so bili modelirani vplivi SP na TMC s pomo~jo ANN in
preiskovana je bila zmo`nost napovedovanja izhodnih parametrov z ANN. Za usposabljanje mre`e je bil razvit algoritem vzvrat-
nega {irjenja napak (BP). Podatki iz eksperimentalnih preizkusov na (TiB + TiC)/Ti–6Al–4V kompozitu so uporabljeni za
usposabljanje mre`e. Volumska dele`a delcev (TiB + TiC) za oja~anje sta bila 5 % in 8 %. ANN preizku{anje je bilo izvedeno z
uporabo razli~nih eksperimentalnih podatkov, ki niso bili uporabljeni pri usposabljanju mre`e. Razdalja od povr{ine (globina) in
intenziteta SP sta uporabljeni kot vhodna parametra, preostala, napetost in trdota Ti–6Al–4V, pred in po SP, in dodatku delcev za
oja~anje, sta izbrana kot izhodna parametra mre`e. Izvedena je bila primerjava med eksperimentalnimi in predvidenimi podatki.
Predvideni rezultati so se dobro ujemali z eksperimentalnimi, kar ka`e na to, da se razvito nevronsko mre`o lahko uporabi pri
modeliranju SP postopka na TMC.
Klju~ne besede: kompoziti na osnovi titana, obdelava povr{ine, hladno kovanje povr{ine, umetna nevronska mre`a, zaostale
napetosti, trdota
1 INTRODUCTION
Titanium matrix composites (TMCs) have attracted
considerable interest due to their attractive properties
over titanium alloys, such as high elastic modulus, high
strength, superior creep and fatigue resistances at
ambient and elevated temperatures.1–4 The fabrication of
TMCs using in-situ technology is simple and does not
result in the pollution of an interface.5,6 TMCs can be
reinforced with continuous fibers, whiskers or particles.7
As is well known, the mechanical properties of the com-
posites depend on matrix, reinforcement and reinforce-
ment/matrix interface, which bonds the formers to-
gether.8 Compared with continuous fibers, TMCs rein-
forced with whiskers or particles exhibit more isotropic
behaviors. The fabrication of these materials is more
convenient and cost effective; therefore, they have drawn
extensive attention recently.9 Titanium monoboride (TiB)
whiskers and titanium carbide (TiC) particles offer high
modulus, relative chemical stability, and high thermal
stability, while maintaining similar density and thermal
expansion coefficient to those of the titanium matrix, as
well as clean interfaces without any unfavorable reaction
between the precipitates and the titanium matrix.10–12 The
Materiali in tehnologije / Materials and technology 50 (2016) 6, 851–860 851
UDK 62-4:669.018.25:004.032.26 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 50(6)851(2016)
reinforcements were obtained according to the high-tem-
perature reactions as follows in Equations (1) and (2):13,14
5Ti+B4C = 4TiB+TiC (1)
Ti+C = TiC (2)
TMCs co-reinforced with TiB whiskers and TiC
particles have been fabricated and investigated for their
mechanical properties15–17 and have been extensively
demonstrated to possess superior mechanical properties
over the single TiB or TiC reinforced discontinuously
reinforced titanium matrix composites (DRTMCs).18–21
As an effective and important surface-treatment
method, shot peening (SP) can introduce high residual
compressive stress (RCS) and microstructure variation at
near surface layers, which can enhance their fatigue pro-
perties compared to non-peened materials. The process
of SP involves the bombardment of spherical balls of a
hard material against the surface of components, which
induces the strong elastic–plastic deformation at the sur-
face and sub-surface regions. In the deformation layers,
high RCS and microstructure refinements are introduced
after SP. The residual stresses and hardness are very
important properties of materials after the SP treatment.
In the field of science and engineering, artificial
neural networks (ANNs) are some of the most important
research areas. ANN is a modeling tool to solve linear
and nonlinear multivariate regression problems.22
Recently, ANN models were widely utilized to interpret
and correlate the variable relationships in complex non-
linear data sets. The present study proposes a new
approach based on ANNs to investigate the effects of SP
process on mechanical and metallurgical properties (TiB
+ TiC)/Ti–6Al–4V composite. Residual stress and hard-
ness were modeled by ANN. 20 data of experimental
tests results from the total of 30, are used to train the
networks, while in the networks testing 10 different
experimental data which were not used during training
are used. Since the experimental results did not include
the training sets the performance of the ANN is eva-
luated in a fine way.
2 EXPERIMENTAL PART
The experimental data are obtained from Xie et al.23
The materials of (TiB + TiC)/Ti–6Al–4V (TiB:TiC = 1:1
(vol.%)) were fabricated via in-situ technology. Two
types of theoretical total volume fraction of reinforce-
ments (TiB + TiC) were 5 % and 8 %. The SP treatment
was performed using an air-blast machine. The related
information of used SP process is demonstrated in Table 1.
The Almen specimens are A type and the diameter of
peening nozzle was 15 mm and the distance between
nozzle and sample was 100 mm. In order to obtain the
depth distribution of the residual stress and hardness, the
thin top surface layers were removed one by one via the
method of chemical etch with a solution of water, nitric
acid, and hydrofluoric acid in the ratio 31:12:7. All the
measurements were carried out at room temperature. The
method of residual stress and hardness measurements are
X ray stress analysis and digital microhardness test res-
pectively.23
Table 1: Parameters of the SP process treatments23
Tabela 1: Parametri uporabljenega procesa SP23
SP
intensity
(mm A)
Shot
material
Shot
diameter
(mm)
Shot
hardness
(HV)
Jet
pressure
(MPa)
SP time
(min)
Cover-
age
(%)
0.15 Caststeel 0.6 610 0.2 0.50 100
0.30 Caststeel 0.6 610 0.3 0.50 100
The results indicate that the increased reinforcements
and SP intensities enhance the surface roughness after
SP. Both the compressive residual stresses and hardness
increase with the increase of the SP intensity, which is
mainly due to the plastic deformation and high disloca-
tion density in the near surface layer. Moreover, the rein-
forcement particles can act as the block sources during
dislocation movements. After an appropriate SP treat-
ment, the increased CRS and hardness are beneficial to
industrial applications A table shows the obtained values
of the experimental results on (TiB + TiC)/Ti–6Al–4V
for 30 different samples. The SP intensity for non-
peened specimens has been shown by zero in Table 2.
3 ARTIFICIAL NEURAL NETWORKS
Artificial intelligence (AI) systems such as artificial
neural networks (ANNs) have found many applications
in science and engineering problems in the past decade.
The concept of an ANN has emerged with the idea that it
E. MALEKI, A. ZABIHOLLAH: MODELING OF SHOT-PEENING EFFECTS ON THE SURFACE PROPERTIES ...
852 Materiali in tehnologije / Materials and technology 50 (2016) 6, 851–860
Figure 1: Schematic of neuron: a) a biological neuron, b) an artificial
neuron
Slika 1: Shematski prikaz nevrona: a) biolo{ki nevron, b) umetni ne-
vron
simulates the operating principles of a human brain. The
first studies were made with mathematical modeling of
biological neurons that make up the brain cells.24 Basi-
cally, the brain functions with a very dense network of
neurons. The brain contains a lot of neurons connected to
each other by many interconnections. A neuron consists
mainly of the following parts: dendrite, cell body and
axon.25 Dendrite gets the signals from various other
neurons to the neuron and carries them to the cell body
for processing, after that an axon carries the signal from
the cell body to various other neurons. Similarly, the
neural units in the artificial neural network are developed
as a very approximate model of the natural biological
neurons.26 Figure 1 shows a natural biological neuron
(Figure 1a) and an artificial neuron (Figure 1b) that is a
computational and mathematical model of the biological
neuron. A single neuron computes the sum of its inputs,
which are multiplying with a variant called the weight,
adds a bias term, and drives the result through a
generally nonlinear transfer function to produce a single
output termed the activation level of the neuron.
An ANN model is created by interconnection of
many of the neurons in a known configuration. The
primary elements characterizing the neural network are
the distributed representation of information, local
operations and non-linear processing. Structurally, every
ANN is made up of three sections: input, hidden and
output layers.27 The structure of an ANN model is deter-
mined by the number of its layers and the number of
nodes in each layer and the nature of the transfer
function.28,29 Selecting the optimum architecture of the
network is one of the challenging steps in ANN mo-
deling. The term “architecture” refers to the number of
layers in the network and the number of neurons in each
layer. However, there is no straightforward method to
estimate the optimal number of hidden layers and neu-
rons in each layer.30,31 Thus trial-and-error methods have
been used by many researchers to determine such case-
dependent parameters for studies involving ANN-based
models.32 Figure 2 represents the architecture of the
neural network. In this network, each input consists of r
parameters and each output comprises s parameters,
E. MALEKI, A. ZABIHOLLAH: MODELING OF SHOT-PEENING EFFECTS ON THE SURFACE PROPERTIES ...
Materiali in tehnologije / Materials and technology 50 (2016) 6, 851–860 853
Table 2: Values of the SP process effects on residual stress and hardness of (TiB + TiC)/Ti–6Al–4V Composite specimens23
Tabela 2: Vrednosti SP postopka, ki vplivajo na zaostale napetosti in trdoto (TiB + TiC) / Ti-6Al-4V kompozitnih vzorcev23
Sample No. Depth SP intensity(mm A)
Residual Stress (MPa) Hardness (HV)
matrix
5 %
(TIB+TIC)
8 %
(TIB+TIC)
matrix
5 %
(TIB+TIC)
8 %
(TIB+TIC)
1 0 0.00 10.42 18.04 17.93 334.72 380.37 417.57
2 0 0.30 -522.83 -524.25 -575.51 524.87 560.38 637.31
3 0 0.15 -375.97 -434.55 -481.94 484.31 512.07 584.43
4 15 0.00 25.11 5.022 6.84 328.67 393.61 436.62
5 15 0.30 -613.76 -648.62 -657.79 436.11 512.19 628.86
6 15 0.15 -417.53 -499.54 -539.63 418.45 492.85 523.28
7 25 0.00 -9.57 -20.26 -12.97 325.48 381.28 420.16
8 25 0.30 -608.67 -650.57 -672.54 414.97 468.23 557.85
9 25 0.15 -408.92 -465.67 -574.80 387.62 451.56 507.09
10 50 0.00 14.35 -29.48 -9.19 315.39 403.32 411.77
11 50 0.30 -581.27 -608.46 -626.77 378.62 455.55 530.79
12 50 0.15 -397.63 -419.90 -545.84 372.53 431.43 475.18
13 75 0.00 14.48 14.02 -12.72 338.28 381.40 423.67
14 75 0.30 -564.84 -570.02 -586.49 385.38 438.64 538.40
15 75 0.15 -354.00 -386.95 -516.88 358.29 420.55 446.63
16 100 0.00 -12.84 -17.01 -14.41 340.03 396.67 414.43
17 100 0.30 -557.53 -524.25 -515.10 368.47 433.57 509.66
18 100 0.15 -324.71 -337.52 -264.28 349.94 411.35 459.31
19 150 0.00 -5.26 -11.81 -8.67 330.01 375.66 409.48
20 150 0.30 -422.37 -335.69 -299.08 350.72 388.76 438.64
21 150 0.15 -302.74 -249.65 -120.90 340.80 386.23 435.87
22 200 0.00 16.96 -13.89 -4.75 319.14 386.77 429.04
23 200 0.30 -323.74 -220.36 -101.37 354.10 402.29 434.42
24 200 0.15 -236.84 -194.73 -61.16 344.29 382.99 424.21
25 250 0.00 28.21 14.93 17.41 337.86 375.06 424.09
26 250 0.30 -46.11 -20.82 -28.14 343.11 380.31 428.50
27 250 0.15 -31.80 -18.99 -15.97 336.83 378.90 410.87
28 300 0.00 -13.62 -23.50 21.33 344.74 369.26 414.91
29 300 0.30 -35.15 -18.99 -33.63 324.51 381.15 430.88
30 300 0.15 -18.99 -11.67 -16.23 326.86 376.50 419.41
while p, w, b, f and a represent the inputs, weight
matrixes, bias vectors, transfer function in neurons, and
outputs, respectively.33
Mathematically, a layer n may be described by
Equations (3) and (4):34
u w ps
n
s
n
i
r
i=
=
∑
1
(3)
a f v f u bs s
n
s
n
s
n= = +( ) ( ) (4)
where p1, p2, . . ., pr are the input signals, wk1, wk2, . . .,
wns are the synaptic weights of neuron n, un is the linear
combiner output due to input signals, bn is the bias, f is
the transfer function and a1, a2, . . ., as are the output
signals of the neuron. The tangent sigmoid (Tansig)
	(x), logarithmic sigmoid (Logsig) 
(x) and linear (x)
transfer function are described as follows in Equations
(5), (6) and (7):35
	( )x
e x
=
+
−−
2
1
12 (5)

( )x
e x
=
+ −
2
1
(6)
( ) ( )x linear x= (7)
3.1 Training of ANN
The training of the ANN is performed by adjusting
the connection weights. It is performed by iteratively
adjusting the weights (w) of the connections and biases
(b) in the network in order to minimize a predefined cost
function.36 The ANNs are trained with a training set of
input and known output data. An ANN is better trained
as more input data are used. The performance of an ANN
is generally based on the parameters’ architecture and the
setting. As was mentioned, one of the most difficult tasks
in studying ANNs is finding an appropriate architecture.
This task is performed via trial and error and the number
of middle layers and neuron presented in each layer is
being identified. Appropriate designation of the initial
amounts of weights and biases is very effective on the
performance of network and the time of calculation. But
there is not a reasonable law and process to identify a
suitable architecture. The only step which is very time
consuming is the trial and error. One can get an idea by
looking at a problem and decide to start with simple
networks; going on to complex ones until the solution is
within acceptable limits of uncertainty. Furthermore, the
point that must be considered in training of the network
is the rate of input and output data scattering. In this
study all values of each input and output data parameters
are divided to maximum absolute value of them and
normalized also the used data are dimensionless. The
normalized data are in range of [–1, +1]. In the present
study, a feed forward ANN based on back propagation
(BP) error algorithm, which is the most popular one in
training of ANNs is used. BP is a descent algorithm,
which attempts to minimize the error during iterations.
The weights of the network are adjusted by the algorithm
such that the error is decreased along a descent direction.
In the back-propagation learning, the actual outputs are
compared with the target values to derive the error
signals, which are propagated backward layer by layer
for the updating of the synaptic weights in all the lower
layers.
E. MALEKI, A. ZABIHOLLAH: MODELING OF SHOT-PEENING EFFECTS ON THE SURFACE PROPERTIES ...
854 Materiali in tehnologije / Materials and technology 50 (2016) 6, 851–860
Figure 3: A Conceptual structure of network with four layers
Slika 3: Konceptualna zgradba mre`e s {tirimi nivoji
Figure 2: Architecture of neural network33
Slika 2: Zgradba nevronske mre`e33
3.2 Implementation of ANN
In this paper the effects of the SP process on surface
properties including of (TiB + TiC) / Ti–6Al–4V com-
posite were modeled by means of an ANN. In implemen-
tation of the ANN distance from the surface (depth) and
SP intensity are regarded as inputs and the residual stress
and hardness are gathered as outputs of the networks.
Different networks with different architecture and net-
work parameters were trained for the prediction of resi-
dual stress and hardness. Figure 3, for an example, re-
presents the schematic architecture of ANN for modeling
of the mentioned output parameters: a four-layer feed
forward with BP algorithm with full interconnection.
This neural network model has a powerful input-output
mapping capability. With the use of enough hidden
neurons, it can effectively approximate any continuous
nonlinear function. In the considered network, two inputs
are logged into the input layer to determine the two
outputs. In the ANN methodology, the sample data is
often subdivided into training and testing sets. The
distinctions among these subsets are crucial.37 Ripley
defines the following: Training set: a set of examples
used for learning that is to fit the parameters of the
classifier. Testing set: a set of examples used only to
assess the performance of a fully-specified classifier.
3.3 Performance evaluation of ANN
The performance of the ANN models in predicting
the shot-peening effects on residual stress and hardness
of (TiB + TiC)/Ti–6Al–4V composite were statistically
evaluated using four prediction score metrics calculated
from the test dataset: Pearson coefficient of correlation
(PCC), root mean square error (RMSE), mean relative
error (MRE) and mean absolute error (MAE). These
parameters were determined using the following
Equations (8), (9), (10) and (11):
PCC
f F f F
f F
EXP i EXP ANN i ANN
i
n
EXP i EXP
=
− − −
−
=
∑ ( ) ( )
( )
, ,
,
1
2 − −
=
∑ ( ),f FANN i ANN
i
n
2
1
(8)
RMSE
f f
n
EXP i ANN
i
n
=
−
=
∑ ( ), 2
1
(9)
MRE
n
f f
f
EXP i ANN
EXP ii
n
=
−
×
=
∑1 1001
1
, ,
,
(10)
MRE
n
f fEXP i ANN
i
n
= −
=
∑1 1
1
, , (11)
where n is the number of used sample for modeling, fEXP
is the experimental value and fANN is the networks
predicted value. Also, the values of FEXP and FANN are
calculating as follows in Equations (12) and (13):
F
n
fEXP EXP i
i
n
=
=
∑1
1
, (12)
F
n
fANN ANN i
i
n
=
=
∑1
1
, (13)
3.4 Generating model function
After the neural network is trained successfully with
four layers, the values of the four parameters of the net-
work (p, b, w and f) can be obtained. The function that
correlates the inputs to the corresponding output can be
calculated by applying the aforementioned parameters.
Finally, the model function can determined in Equations
(14) and (15):
a1= f1(w1p+b1) (14a)
a2= f2(w2p1+b2) (14b)
a3= f3(w3p2+b3) (14c)
a4= f4(w4p3+b4) (14d)
G (g(1), g(2))= a4=
= f4(w4f3 (w3 2(w2f1(w1p+b1)+ b2) +b3)+ b4) (15)
where a1, a2 and a3 are the outputs of the first, second
and third layer, respectively; a4 is the fourth layer out-
put, which is equal to the function G (g(1), g(2)). The
function G gets the values of the input parameters. The
function of g(1)and g(2) represent the residual stress
and hardness, respectively. The methodology used for
neural network application in this study is as follows:
1. Start;
2. Normalize the data (inputs & outputs);
3. Feed the data to artificial neural network;
4. Find network optimum parameters;
5. Execute network training;
6. Obtain Pearson correlation coefficient;
7. If PCC = 0.99 go to 8, if not go back to 4 with re-
vising the parameters of network;
8. Continue processing until obtaining desired conver-
gence between experimental and predicted values;
9. Obtain weights & biases values;
10. Create the model function;
11. Conduct analysis based on model function;
12. Verify the results using experimental values;
13. Calculate the error for each answer;
14. End.
4 RESULTS AND DISCUSSION
In order to train the ANNs in this study, the obtained
experimental test results on shot peened (TiB +
TiC)/Ti–6Al–4V composite specimens are employed.
Different networks were trained to achieve the optimum
structure (OS) in order to generate a model function
(MF). After the OS is selected and the MF is generated,
operation of the network is tested with the use of them
(OS & MF). Twenty sample data (data of samples 1-20)
E. MALEKI, A. ZABIHOLLAH: MODELING OF SHOT-PEENING EFFECTS ON THE SURFACE PROPERTIES ...
Materiali in tehnologije / Materials and technology 50 (2016) 6, 851–860 855
were used from the total of 30, as data sets for network
training. Table 3 shows the normalized sample data used
for networks training. In the network testing, 10 different
sample data (data of samples 21–30) which were not
used during training are employed. Therefore, the whole
experimental results did not comprise in the training. For
investigative purposes, out of 30 samples data, 67 % data
had taken for training and 33 % data for testing. Several
networks have been trained with different architecture to
find the OS of ANNs, to predict the regarded outputs,
with the best performance and the highest PCC, the least
RMSE, MRE and MAE. Related information of some
the different trained networks for modelling of matrix
hardness are shown in Table 4. The ordinal numbers
shown in the "Layer Structure" were used to indicate the
total number of neurons in the input, hidden and output
layers, respectively. Results of the networks were investi-
gated and the ANN modelling number 11 with
2×8×16×2 structure is selected for modelling and simu-
lation.
Figures 4 and 5 show the obtained values of the
ANN response in comparison with experimental values
for each 20 training samples (samples 1–20) for residual
stress and hardness, respectively, using the selected
network.
After the network was trained, the selected network is
tested. Figures 6 and 7 have been demonstrated the
predicted and experimental values of residual stress and
hardness for 10 different testing samples (samples
21–30) respectively.
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856 Materiali in tehnologije / Materials and technology 50 (2016) 6, 851–860
Table 3: Normalized sample data used for networks training
Tabela 3: Normalizirani podatki vzorca, uporabljenega pri usposabljanju mre`e
Sample No. Depth SP intensity
Residual stress Hardness
matrix 5 %(TIB+TIC)
8 %
(TIB+TIC) matrix
5 %
(TIB+TIC)
8 %
(TIB+TIC)
1 0.0000 0.0 0.0170 0.0277 0.0267 0.6377 0.6788 0.6552
2 0.0000 1.0 -0.8518 -0.8058 -0.8557 1.0000 1.0000 1.0000
3 0.0000 0.5 -0.6126 -0.6680 -0.7166 0.9227 0.9138 0.9170
4 0.0500 0.0 0.0409 0.0077 0.0102 0.6262 0.7024 0.6851
5 0.0500 1.0 -1.0000 -0.9970 -0.9781 0.8309 0.9140 0.9867
6 0.0500 0.5 -0.6803 -0.7678 -0.8024 0.7972 0.8795 0.8211
7 0.0833 0.0 -0.0156 -0.0311 -0.0193 0.6201 0.6804 0.6593
8 0.0833 1.0 -0.9917 -1.0000 -1.0000 0.7906 0.8356 0.8753
9 0.0833 0.5 -0.6663 -0.7158 -0.8547 0.7385 0.8058 0.7957
10 0.1667 0.0 0.0234 -0.0453 -0.0137 0.6009 0.7197 0.6461
11 0.1667 1.0 -0.9471 -0.9353 -0.9319 0.7214 0.8129 0.8329
12 0.1667 0.5 -0.6479 -0.6454 -0.8116 0.7098 0.7699 0.7456
13 0.2500 0.0 0.0236 0.0216 -0.0189 0.6445 0.6806 0.6648
14 0.2500 1.0 -0.9203 -0.8762 -0.8721 0.7342 0.7828 0.8448
15 0.2500 0.5 -0.5768 -0.5948 -0.7685 0.6826 0.7505 0.7008
16 0.3333 0.0 -0.0209 -0.0261 -0.0214 0.6478 0.7079 0.6503
17 0.3333 1.0 -0.9084 -0.8058 -0.7659 0.702 0.7737 0.7997
18 0.3333 0.5 -0.5291 -0.5188 -0.3930 0.6667 0.7341 0.7207
19 0.5000 0.0 -0.0086 -0.0182 -0.0129 0.6287 0.6704 0.6425
20 0.5000 1.0 -0.6882 -0.5160 -0.4447 0.6682 0.6937 0.6883
Table 4: Relevant information of 12 different networks for modeling of matrix hardness
Tabela 4: Pomembne informacije o 12 razli~nih mre`ah pri modeliranju trdote osnove
ANN
Modeling no.
Rate of
training
Layers
structure
Hidden transfer
function
Output transfer
function PCC RMSE MRE (%) MAE
1 0.090 2×2×4×2 Logsig Linear 0.97035 0.7677 0.1552 0.6680
2 0.095 2×2×6×2 Tansig Linear 0.97421 0.7018 0.1399 0.5742
3 0.110 2×2×8×2 Logsig Tansig 0.98460 0.6671 0.1007 0.5018
4 0.100 2×4×4×2 Tansig Linear 0.98662 0.4163 0.0938 0.4261
5 0.115 2×4×6×2 Logsig Linear 0.99003 0.2397 0.0875 0.3459
6 0.120 2×4×10×2 Logsig Linear 0.99150 0.2078 0.0617 0.2822
7 0.115 2×6×10×2 Tansig Tansig 0.99877 0.3400 0.0587 0.2401
8 0.130 2×6×12×2 Tansig Linear 0.99901 0.2229 0.0461 0.1886
9 0.145 2×6×16×2 Logsig Tansig 0.99936 0.1997 0.0384 0.1597
10 0.160 2×8×10×2 Logsig Logsig 0.99911 0.1609 0.0331 0.1529
11 0.165 2×8×16×2 Logsig Logsig 0.99979 0.0985 0.0194 0.0853
12 0.165 2×8×20×2 Tansig Linear 0.99963 0.1265 0.0247 0.1173
E. MALEKI, A. ZABIHOLLAH: MODELING OF SHOT-PEENING EFFECTS ON THE SURFACE PROPERTIES ...
Materiali in tehnologije / Materials and technology 50 (2016) 6, 851–860 857
Figure 7: Comparison of predicted values (ANN response) with experimental values for each 20 testing samples (samples 21–30) for hardness:
a) matrix, b) 5 % TIB+TIC and c) 8 % TIB+TIC
Slika 7: Primerjava napovedanih vrednosti (odgovor ANN) z eksperimentalnimi vrednostmi za vsakega od 20 preizku{enih vzorcev (vzorci
21-30) za trdoto: a) osnova, b) 5 % TiB+TiC in c) 8 % TiB+TiC
Figure 6: Comparison of predicted values (ANN response) with experimental values for each 20 testing samples (samples 21–30) for residual
stress: a) matrix, b) 5 % TIB+TIC and c) 8 % TIB+TIC
Slika 6: Primerjava napovedanih vrednosti (odgovor ANN) z eksperimentalnimi vrednostmi za vsakega od 20 preizku{enih vzorcev (vzorci
21-30) za zaostale napetosti: a) osnova, b) 5 % TiB+TiC in c) 8 % TiB+TiC
Figure 5: Comparison of predicted values (ANN response) with experimental values for each 20 training samples (samples 1–20) for hardness: a)
matrix, b) 5 % TiB+TiC and c) 8 % TiB+TiC
Slika 5: Primerjava napovedanih vrednosti (odgovor ANN) z eksperimentalnimi vrednostmi za vsakega od 20 vzorcev usposabljanja (vzorci
1-20) za trdoto: a) osnova, b) 5 % TiB+TiC in c) 8 % TiB+TiC
Figure 4: Comparison of predicted values (ANN response) with experimental values for each 20 training samples (samples 1–20) for residual
stress: a) matrix, b) 5 % TiB+TiC and c) 8 % TiB+TiC
Figure 4: Primerjava napovedanih vrednosti (odgovor ANN) z eksperimentalnimi vrednostmi za vsakega od 20 vzorcev usposabljanja (vzorci
1-20) za zaostale napetosti: a) osnova, b) 5 % TiB+TiC in c) 8 % TiB+TiC
Figure 8 illustrates the obtained relative error (RE)
values of the residual stress and hardness for the testing
samples. In modeling of residual stress, according to the
Figure 8a, the minimum and maximum (min., max.)
determined relative errors for matrix, 5 % reinforcement
and 8 % reinforcement are (0.000,0.2633), (0.0103,
0.1714) and (0.0099, 0.2616), respectively. Based on
Figure 8b, similarly minimum and maximum calculated
REs for matrix, 5 % reinforcement and 8 % reinforce-
ment in modeling of hardness are (0.0015, 0.0587),
(0.0026, 0.0870) and (0.0023, 0.0919), respectively.
According to the obtained values of the ANN for
training and testing samples, data corresponding to the
used network are shown in Table 5.
In network training it is observed that the values of
PCC for each considered output parameters are more
than 99.7 %. The values of training RMSE, MRE and
E. MALEKI, A. ZABIHOLLAH: MODELING OF SHOT-PEENING EFFECTS ON THE SURFACE PROPERTIES ...
858 Materiali in tehnologije / Materials and technology 50 (2016) 6, 851–860
Figure 9: Distribution of residual stresses along the depth from the
surface obtained by OS and MF of ANN for different SP intensities of:
a) 0 mm A, b) 0.15 mm A and c) 0.3 mm A
Slika 9: Razporeditev spreminjanja zaostalih napetosti v globino od
povr{ine, dobljene pri OS in MF z ANN pri razli~nih intenzitetah SP:
a) 0 mm A, b) 0,15 mm A in c) 0,3 mm A
Figure 8: Values of obtained relative error for testing samples (sam-
ples 21–30) for considered output parameters: a) residual stress, b)
hardness
Slika 8: Vrednosti dobljene relativne napake preizku{anih vzorcev
(vzorci 21-30) pri upo{tevanih izhodnih parametrih: a) zaostale nape-
tosti, b) trdota
Table 5: Obtained values of PCC, RMSE, MRE and MAE for trained and tested network
Tabela 5: Dobljene vrednosti PCC, RMSE, MRE in MAE pri usposobljeni in pri preizku{eni mre`i
Output
parameter
Training Testing
PCC RMSE MRE (%) MAE PCC RMSE MRE (%) MAE
Residual
stress
Matrix 0.99914 0.1781 0.1104 0.1099 0.99846 0.2529 0.1223 0.1315
5 % rein. 0.99875 0.0651 0.0872 0.0471 0.99816 0.0906 0.0910 0.0521
8 % rein. 0.99766 0.0597 0.1228 0.0382 0.99683 0.0647 0.1342 0.0440
Hardness
Matrix 0.99979 0.0985 0.0194 0.0853 0.99912 0.1154 0.0276 0.0937
5 % rein. 0.99901 0.1544 0.0313 0.1372 0.99858 0.1783 0.0368 0.1420
8 % rein. 0.99837 0.1976 0.0346 0.1475 0.99721 0.2071 0.0419 0.1780
MAE are very close to 0 and they are in little intervals
and their ranges are [0.0597, 0.1976], [0.0194, 0.1228]
and [0.0382, 0.14715], respectively. So, it is concluded
that networks are trained finely and adjusted carefully.
Likewise in network testing the values of PCC are more
than 99.6 % and it is observed that values of testing PCC
have a negligible reduction in comparison with the train-
ing. Moreover, the values of testing RMSE, MRE and
MAE are in a tiny span as well and their ranges are
[0.0647, 0.2071], [0.0276, 0.1342] and [0.0440, 0.1780],
respectively. Based on the achieved values for the
statistical errors for both training and testing samples it
is concluded that the error values are acceptable and
implementation of ANN is accomplished in a good way.
In residual stress modeling for each case of network
training and testing, the obtained values for 5 % TiB +
TiC., matrix and 8 % TiB + TiC and in modeling of
hardness, achieved values for matrix, 5 % TiB + TiC and
8 % TiB + TiC have the smallest errors, respectively.
Distributions of the residual stress and hardness from the
shot-peened surface to the bulk material (25-300 μm) for
SP intensity of (0.00, 0.15 and 0.30) are shown in
Figures 9 and 10, which are achieved by OS and MF of
the used ANN modeling in this paper.
5 CONCLUSION
In present study the application of ANNs was
investigated, aiming to create models to predict and
optimize the SP process effects with different intensities
on the residual stress and hardness of a (TiB +
TiC)/Ti–6Al–4V composite. Experimental data show
that both the residual stress and the hardness were
increased with an improvement of the SP intensities.
Residual stress and hardness were modeled using ANN
for three cases: matrix, 5 % TiB + TiC and 8 % TiB +
TiC. The obtained results indicate that statistical errors
for RSME, MRE and MAE are in very small range and
so close to 0. Moreover, the values of PCC for all of the
regarded output parameters in implemented networks are
more than 99 %. According to the achieved results, it can
be concluded that when the ANNS are tuned in a good
way and adjusted carefully, the modeling results are in
reasonable agreement with the experimental results.
Therefore, using ANNs, instead of costly and time
consuming experiments, decreases the costs and the need
for special testing facilities, and the ANNs can be
employed to predict and optimize the SP effects on the
residual stress and the hardness of TMCs.
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