An intelligent system for squeeze casting process—soft computing based approach

Abstract

The present work deals with the forward and reverse modelling of squeeze casting process by utilizing the neural network-based approaches. The important quality characteristics in squeeze casting, namely surface roughness and tensile strength, are significantly influenced by its process variables like pressure duration, squeeze pressure, and pouring and die temperatures. The process variables are considered as input and output to neural network in forward and reverse mapping, respectively. Forward and reverse mappings are carried out utilizing back propagation neural network and genetic algorithm neural network. For both supervised learning networks, batch training is employed using huge training data (input-output data). The input-output data required for training is generated artificially at random by varying process variables between their respective levels. Further, the developed model prediction performances are compared for 15 random test cases. Results have shown that both models are capable to make better predictions, and the models can be used by any novice user without knowing much about the mechanics of materials and the process. However, the genetic algorithm tuned neural network (GA-NN) model prediction performance is found marginally better in forward mapping, whereas BPNN produced better results in reverse mapping.

Full text

ORIGINAL ARTICLE
An intelligent system for squeeze casting process—soft computing
based approach
Manjunath Patel G. C.
1
&Prasad Krishna
1
&Mahesh B. Parappagoudar
2
Received: 2 November 2014 /Accepted: 20 January 2016
#Springer-Verlag London 2016
Abstract The present work deals with the forward and re-
verse modelling of squeeze casting process by utilizing the
neural network-based approaches. The important quality char-
acteristics in squeeze casting, namely surface roughness and
tensile strength, are significantly influenced by its process
variables like pressure duration, squeeze pressure, and
pouring and die temperatures. The process variables are con-
sidered as input and output to neural network in forward and
reverse mapping, respectively. Forward and reverse mappings
are carried out utilizing back propagation neural network and
genetic algorithm neural network. For both supervised learn-
ing networks, batch training is employed using huge training
data (input-output data). The input-output data required for
training is generated artificially at random by varying process
variables between their respective levels. Further, the devel-
oped model prediction performances are compared for 15 ran-
dom test cases. Results have shown that both models are ca-
pable to make better predictions, and the models can be used
by any novice user without knowing much about the mechan-
ics of materials and the process. However, the genetic algo-
rithm tuned neural network (GA-NN) model prediction
performance is found marginally better in forward mapping,
whereas BPNN produced better results in reverse mapping.
Keywords Squeeze casting process .Forward mapping .
Reverse mapping .BPNN and GA-NN
1 Introduction
The near net-shape manufacturing capability of the squeeze
casting process has greater potential to yield good-quality cast-
ings. In squeeze casting, the casting quality is mainly affected
by cold laps, segregations (types such as v-type, minor, macro,
pipe, centreline, extrusion), hot tears, sticking, over filling, un-
der filling, case de-bonding, shrinkage and so on [1,2]. It is
noteworthy that accurate control of process variables is one of
the possible solutions to reduce defects and to obtain the desir-
able quality in castings (surface finish and tensile strengths). A
great deal of research work was carried out in this arena, during
the 1990s and 2000s throughout the world. However, majority
of work reported in the literatures during that period was on use
of numerical, analytical, and classical experimental approaches.
The effects of casting temperature on the mechanical properties
were investigated by Yang [3]. The influence of die tempera-
ture, squeeze pressure and pressure durations were kept con-
stant in their study. Further, analytical models, such as gracia’s
virtual and steady state heat flow models were utilized to esti-
mate the influence of solidification time towards the mechani-
cal properties [4]. A major drawback of their model is that the
analysis was carried out with many assumptions. The pouring
temperature and squeeze pressure influences on the mechanical
properties were studied [5,6]. It is to be noted that pressure
duration and die temperature effects were not considered in
their analysis. The influencing process variables such as
squeeze pressure and pouring and die temperatures were
*Mahesh B. Parappagoudar
maheshpg@gmail.com
Manjunath Patel G. C.
manju09mpm05@gmail.com
Prasad Krishna
krishnprasad@gmail.com
1
Department of Mechanical Engineering, National Institute of
Technology Karnataka, Surathkal 575025, India
2
Department of Mechanical Engineering, Chhatrapati Shivaji Institute
of Technology, Durg, C. G. 491001, India
Int J Adv Manuf Technol
DOI 10.1007/s00170-016-8416-8

studied to investigate their effects on the mechanical and micro-
structure properties [7]. It must be duly noted that experiments
were conducted with the constant pressure duration. Although
much work is reported earlier in the literature to improve the
casting quality, the practical guidelines followed by the re-
searchers may not be sufficient to the foundry men in selecting
the most influential parameters.
The Taguchi method and statistical design of experiments
have been used in the past, wherein the process parameters
were simultaneously varied. The main and combined process
parameter effects were identified and analyzed. The complex
input-output relationships were established at reduced cost
and energy consumption. The Taguchi method was adopted
to study the effects of die materials, die temperature and
squeeze pressure on the surface roughness of the LM24 alloy
[8]. It is to be noted that experiments were carried out by
keeping the pressure duration and pouring temperature as a
constant. To study the effects on mechanical properties of
aluminium and magnesium-based alloys [9,10], the influence
of die temperature, applied pressure and its durations were
considered. It is to be noted that pouring temperature contri-
butions were left out in their research work. Squeeze pressure
and pouring and die temperature effects were studied to esti-
mate the percent contribution of process variables on surface
roughness (SR), density, hardness and ultimate tensile
strengths (UTS) of aluminium alloys [11,12]. It is also impor-
tant to mention that experiments are conducted for the fixed
pressure duration. Bin et al. [13] studied the strength and duc-
tility of the cast components under the different squeeze pres-
sure, filling velocity, pouring, and mould temperature. It is
noteworthy that the pressure duration effects were not consid-
ered in their analysis. Yield strength (YS) of the cast parts
were studied under different squeeze casting conditions [14].
An attempt was made by authors [15] to improve the ductility
by optimizing melt, die-preheat temperature and squeeze pres-
sure parameters using the statistical Taguchi method.
However, the paramount information regarding the duration
of holding and waiting time has not reported.
The practical requirement for industry personnel is to know
the required process variable combinations that will produce
the desired output, particularly for online process control. An
attempt was made in the past using statistical regression tool to
predict the welding parameters through reverse mapping [16].
Reverse mapping via statistical regression tools requires the
transformation matrix to be a square one. Hence, the model
predictions can be determined only for the response equation
includes linear terms, whereas transformation matrix might not
be invertible with interaction terms in response equation. Thus,
statistical design of experiments and the Taguchi method fails
to perform reverse modelling accurately. Soft computation tools
have been proven to be the cost effective to meet the industrial
requirements, analyze the complex non-linear input-output re-
lationships and predict multi-outputs simultaneously. Artificial
neural networks (ANNs) have been utilized to predict the tem-
perature difference of the squeeze cast part using back propa-
gation algorithms [17]. Later on, the authors extended their
research work to predict the solidification time using ANNs
[18]. The mechanical properties of the squeeze cast parts were
predicted for different squeeze casting conditions using radial
basis functions of ANNs [19]. More recently [20], ANNs were
used to predict the outputs (i.e. density and secondary dendrite
arm spacing) and process parameters (time delay, squeeze pres-
sure, pressure duration, melt and die-preheat temperature) using
forward and reverse mapping tools. It is to be noted that the
training data had been collected, where the interaction terms in
the response equations were neglected. This might have result-
ed in large average absolute percent deviation in prediction. In
the recent past, few authors had used neural networks as for-
ward mapping tool to predict the casting properties for the
known set of process parameters [21–24]. Few researchers
made an attempt to predict the responses as well as process
variables using forward and reverse mappings of neural net-
work approaches [25–29]. Neural network (NN) trained with
back propagation (BP) algorithm has been successfully applied
in the past for prediction. Since the BP algorithm works on the
steepest descent method, it has a greater probability of getting
trapped in local optimum solutions. However, an evolutionary
genetic algorithm (GA) starts searching the solutions in huge
space at many distinct locations, simultaneously. Thus, GA has
greater probability to hit the global minima.
An attempt is being made in the present study to carry out
both forward and reverse mappings utilizing BP algorithm
tuned neural network (BPNN) and GA tuned NN (GA-NN),
separately. The following two objectives are aimed in the
present work:
&Forward mapping: Forward mapping is carried out to pre-
dict the casting properties (surface roughness, yield
strength and ultimate tensile strength) for the known set
of process variables (squeeze pressure, pressure duration,
pouring temperature and die temperature). For the 15 test
cases, neural network models prediction performances are
compared among themselves and those with the statistical
regression models.
&Reverse mapping: Reverse mapping is carried out to predict
the required process variable combination, which will yield
the desired surface roughness, yield and ultimate tensile
strength. It is noteworthy that the prediction performances
are compared among the neural network-based approaches.
2 Modelling of squeeze casting system
Modelling has been employed to map the complex non-linear
system by utilizing neural network-based models. To establish
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the input-output relationships, four process variables have
been considered, namely, pressure duration, squeeze pressure,
pouring temperature, die temperature as input and three con-
flicting (minimization and maximization) responses such as
surface roughness, yield and ultimate tensile strength as out-
put. The process variables and their respective levels consid-
ered for the present work is presented in Table 1.
2.1 Forward mapping
The three-layer feed forward neural network with input, hidden
and output layers is considered (refer to Fig. 1). In the forward
mapping, four and three neurons are used in the input and output
layers to represent the process variables and responses, respec-
tively. The detailed parametric study has been carried out to
optimize NN parameters by varying individual network param-
eter at once after keeping other network parameters at mid-
values. During the first stage of parameter study, hidden neurons
are varied in the range of 4 to 25, and the optimum number of
hidden neuron has been selected corresponding to the minimum
mean squared error. Optimization of other NN parameters, name-
ly, learning rate, momentum constant, constants of activation
function hidden layer, constants of activation function output
layer-1, constants of activation function output layer-2, and bias
value has been carried out in the subsequent stages of parametric
study. The training and testing data are normalized between zero
and one to avoid numerical overflows due to very low and high
values. It is noteworthy that the process parameter effect on the
measured responses has been studied by using surface plots, and
interdependency among the outputs is also checked [30]. A linear
transfer function, y = mx, is employed for the input layer. The
value of m(0 < m> 1) is determined through number of trial runs.
It has been observed that the influence of process variables on
surface roughness is opposite to that of the tensile strengths.
Hence, for the output layer, the following log-sigmoid transfer
functions are used while modelling the responses (Eqs. 1and 2)
Surface roughness;y¼1
1þexp axðÞðÞ ð1Þ
Yield strength;ultimate tensile stength;y
¼1
1þexp −bxðÞðÞ ð2Þ
Log-sigmoid transfer function is employed for all the hid-
den neurons lying in that layer (see Eq. 3)
y¼1
1þexp −cxðÞðÞ ð3Þ
The terms a, b and c are the constants of activation func-
tion; yrepresents the neuron output and xis the neuron input.
The steps followed in modelling the squeeze casting process
for BPNN is shown in Appendix B.
Reverse mapping The requirement to predict the process pa-
rameters for the desired output is carried out utilizing reverse
mapping. BPNN and GA-NN have been used to carry out the
abovementioned task. In the reverse modelling system, the
outputs (casting properties) of the forward mapping are treated
as inputs, and inputs (process variables) are expressed as a
function of outputs.
2.2 Back propagation algorithm tuned neural network
(or) BP algorithm tuned NN
The supervised learning capability of back propagation algorithm
has been adaptively trained with batch mode to reduce the error
in successive iterations. The network predictions obtained by the
forward pass calculation is compared with the target values in
order to determine the error. The mean squared error (MSE) is
used as an error function in the present work is shown in Eq. 4
MSE ¼1
RNX
R
i¼1
X
N
j¼1
1
2Tij−Oij

2ð4Þ
The terms T
ij
and O
ij
depicts the desired (experimental or
target), and the network predicted output values; R denotes the
number of outputs, and N represents the number of network
training scenarios. It is to be noted that network weights are
updated for minimum error using Eq. 5.
ΔWjk tðÞ¼−η∂E
∂Wjk
tðÞþαΔWjk t−1ðÞ ð5Þ
The term ηrepresents the learning rate, t indicates the iter-
ation number and αis the momentum constant. ∂E/∂W
jk
esti-
mated utilizing the chain rule of differentiation (see Eq. 6). Y
k
and U
k
represent output and input, respectively, of k
th
neuron
lying in the output layer.
∂E
∂Wjk
¼∂E
∂Yk
∂Yk
∂Uk
∂Uk
∂Wjk
ð6Þ
2.3 GA tuned NN
The population-based search method i.e. GA has been used in
the past to optimize the complex manufacturing processes. In
the present work, GA has been used to tune the network pa-
rameters, wherein the optimal solutions are searched in multi-
dimensional space at many distinct locations simultaneously.
The auxiliary hybrid working system has been used in the
integral GA-NN model. In GA-NN, the network parameters
such as synaptic weights, bias and transfer function constant
values are supplied through GA-string, and the network com-
putes the expected output. The optimum number of hidden
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neurons, which is determined through a parametric study
using BPNN, is kept the same in combined GA-NN approach.
The mean square error is calculated by comparing the network
predicted and target values. The determined mean squared
error is used as the fitness function for GA-string (refer to
Eq. 7). The schematic diagram of working cycle GA-NN
model is shown in Appendix C. The solutions are altered
using the selected GA parameters namely, bit wise mutation,
uniform cross over and tournament selection.
Fitness ¼1
RNX
R
i¼1
X
N
j¼1
1
2Tij−Oij

2ð7Þ
2.4 Data collection
The training of NN requires huge input-output data base, and
collection of such data through actual experiments is impractical.
Hence, training data is generated at random by utilizing response
equations derived through actual experiments via statistical
modelling. It is important to note that the test case data have been
collected through actual experimentations.
2.5 Training data
Experiments are conducted using standard matrices of statis-
tical design ofexperiments and response surface methodology
(RSM). The non-linear input-output relations (response equa-
tions) have been obtained by conducting experiments and ap-
plying statistical DOE and RSM techniques. These response
equations have been used to artificially generate the training
data, related to the responses such as, surface roughness, yield
and ultimate tensile strengths. To derive, the response equa-
tions two non-linear regression models are used namely box-
behnken design (BBD) and central composite design (CCD)
[30]. Further, the best model for each response has been
Tabl e 1 Process variables and
their respective levels Process variables Levels
Source Un-coded Units Low (−1) Middle (0) High (+1)
Pressure duration A S 20 35 50
Squeeze pressure B MPa 40 80 120
Pouring temperature C °C 630 675 720
Die temperature D °C 150 225 300
Fig. 1 Artificial neural network
structure used for forward
mapping
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selected based on the average absolute percent deviation de-
termined by utilizing the test cases [30]. It is noteworthy that
CCD-based model performs best when modelling for surface
roughness and yield strength, whereas BBD showed a better
result for ultimate tensile strength predictions. Hence, the
input-output data has been artificially generated using the best
regression equations obtained for different responses using
two non-linear regression models is shown in Eqs. 8–10:
SRCCD ¼15:2320−0:0215093A−0:0249583B−0:0376636Cþ0:00577407Dþ2:22222
10−05A2þ6:875 10−05B2þ2:71605 10−05C2−8:88889 10−06D2þ2:70833
10−05AB þ2:40741 10−05AC−2:22222 10−06AD þ2:08333 10−06BC þ1:0833
310−05BD −5:92593 10−06CD
ð8Þ
YSCCD ¼−1071:38−1:26601A−0:797501Bþ3:36494Cþ0:902819Dþ0:0123095A2
þ0:00276227B2−0:00238537C2−8:58733 10−04D2þ0:00253125AB
þ0:000101852AC þ0:000627778AD þ0:000746528BC þ0:00034375BD
−8:87037 10−04CD
ð9Þ
UTSBBD ¼−1176:2−4:71685A−1:29458Bþ3:97148Cþ0:932667D−0:00137037A2
þ0:00234635B2−0:00293004C2−8:21481 10−04D2þ0:00354167AB
þ0:00651852AC þ4:44444 10−05 AD þ0:00155556BC þ0:001025BD
−0:00102693CD
ð10Þ
2.6 Test data
Fifteen test cases are randomly generated after selecting the
process variables between their corresponding levels. The ex-
periments have been conducted to measure the outputs name-
ly, surface roughness, yield strength and ultimate tensile
strength. Three replicates are considered for each casting con-
dition. Average values of nine surface roughness and six ten-
sile strengths are used to minimize the error variations and to
check the prediction performance. The 15 random test cases
which have been utilized to test the prediction performance of
neural network (BPNN and GA-NN) models in forward and
reverse mapping is shown in Appendix A.
3 Results and discussions
In forward mapping case, the prediction performances of
neural network-based approaches have been compared
among themselves and with those of the statistical
design of experiments. The neural network performances
are compared among themselves in reverse mapping. It
is important to note that the same network training and
testing data are used for both forward and reverse map-
pings of neural network-based approaches. The forward
and reverse mappings results will be discussed in the
following sections.
3.1 Results of forward mapping
The neural network (BPNN and GA-NN) models have been
used to predict the surface roughness, yield and ultimate ten-
sile strengths for the known set of process variable combina-
tions namely squeeze pressure, pressure duration, pouring
temperature and die temperature.
3.2 BP algorithm tuned NN
Thousands of combinations of input-output data have
been generated artificially by utilizing the regression
(8)
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equations, and the same is used to train the network
through batch mode. To determine the optimum network
parameters, a detailed parametric study has been con-
ducted as shown in Fig. 2. The results of the parametric
Fig. 2 BPNN parametric study: a
MSE vs. no. of hidden neurons, b
MSE vs. learning rate-hidden
layer, cMSE vs. learning rate-
output layer, dMSE vs.
momentum constant, eMSE vs.
activation function constant-
hidden layer, ferror MSE vs.
activation function constant 1-
output layer, gMSE vs. activation
function constant 2-output layer
and gMSE vs. bias value
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study obtained for an optimum network parameters are
presented in Table 2. The network training is completed
with the minimized mean squared error equal to
0.002961. The trained neural models are tested for 15
test cases, and the results obtained in terms of average
absolute percent deviation in prediction considering all
outputs are found to be equal to 4.87 %.
3.3 GA tuned NN
The GA-NN performance depends mainly on the GA param-
eters namely size of population, probability of mutation and
number of generations. GA parameters are optimized by
conducting the detailed parametric study (refer to Fig. 3).
Uniform cross over with a probability value of 0.5 is used.
The optimized GA parameter values obtained using the para-
metric study is shown in Table 3. The network training com-
pleted with the reduced mean squared error found equal to
0.001338. The average absolute percent deviation in predic-
tion of test cases considering all the responses is found to be
equal to 3.54 %.
Tabl e 2 BPNN parametric study results of both forward mapping
Neural network parameters Optimum parameter values
Hidden neurons 23
Learning rate-hidden layer, η0.455
Learning rate-output layer, η0.4995
Momentum constant, α0.4995
Activation constant-hidden layer 4.15
Activation constant-output layer-1 3.25
Activation constant-output layer-2 5.5
Bias 0.00009505
Fig. 3 GA-NN parametric study aMSE vs. mutation probability (P
m
), bMSE vs. population size and cMSE vs. generation number
Tabl e 3 GA-NN parametric study results of forward mappings
GA-NN parameters Optimum parameter values
Mutation probability 0.0001106
Population size 274
Generations number 510
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3.4 Comparison of forward mapping of neural network
and statistical models
The GA-NN and BPNN prediction performances are
compared among themselves and those with statistical
models for 15 test cases. Figure 4a compares the per-
cent deviation (PD) in prediction of surface roughness
utilizing the three models. Prediction performances of
non-linear regression-based CCD model and GA-NN
are found to be of almost similar. The prediction of
surface roughness in terms of PD values using CCD,
BPNN and GA-NN are found to vary in the range of
−14.86 to +9.59 %, −39.13 to +11.2 % and −15.22 to
+13.7 %, respectively. Similarly, the prediction of yield
strength in terms of percent deviation values using
CCD, BPNN and GA-NN models are found to lie in
the range of −6.67 to +2.3 %, −6.13 to +4.76 % and
−6.35 to +2.67 %, respectively (see Fig. 4b). The non-
linear regression-based BBD model performed better for
predicting the ultimate tensile strengths. The PD in pre-
Fig. 4 Models comparison in terms of PD in prediction asurface roughness, byield strength and cultimate tensile strength
Tabl e 4 Models comparison for
prediction of responses (forward
mapping)
Response Average absolute percent deviation in prediction
BPNN GA-NN CCD [30]BBD[30]
Surface roughness 10.05 6.36 6.48 7.94
Ultimate tensile strength 1.998 2.11 1.94 1.76
Yield strength 2.57 2.16 2.21 3.27
Average of all responses 4.87 3.54 3.54 4.32
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diction of ultimate tensile strength using BBD, BPNN
and GA-NN models are found to vary in the range of
−4.61 to +2.68 %, −2.94 to +4.07 % and −4.15 to
+3.72 %, respectively (refer Fig. 4c).
Tab le 4compares the neural network (BPNN and
GA-NN) models and statistical (CCD and BBD)
models for 15 test cases in terms of average absolute
PD in prediction of the individual and combined re-
sponses. Considering all responses, the average abso-
lute PD in prediction made by BPNN, GA-NN, CCD
and BBD models are found to be equal to 4.87, 3.54,
3.54 and 4.32 %. However, GA-NN performance is
comparable with CCD-based non-linear model and
outperformed other models for predicting the com-
bined responses in terms of average absolute percent
deviation (refer to Fig. 5).
The results have shown that all the models are ca-
pable of making effective prediction; however, GA-NN
performs slightly better compared to BPNN. The rea-
sons might be the ability of the GA to search the
global solutions in multi-dimensional space at many
distinct locations simultaneously and its ability to cap-
ture non-linear information of the process accurately.
The nature of error surface and more importantly due
to the lesser chances of optimum solution getting
trapped in local minima with GA might have resulted
in better performance of GA-NN. In making accurate
predictions, although non-linear regression-based CCD
model is comparable with GA-NN model, the main
weakness of the non-linear regression-based CCD mod-
el is that predictions are made response wise (i.e. one
response at a time). Hence, it fails to capture interde-
pendency among the outputs (if any) since all the re-
sponses are measured on the same sample under par-
ticular casting conditions.
3.5 Results of reverse mapping
The stringent requirement for the industrial personnel to
know the required process parameters setting in order to
obtain the desired responses is carried out through the
reverse mappings, using neural network-based ap-
proaches. It is to be noted that during training, surface
roughness, ultimate tensile strength and yield strength
are used as the network inputs to predict the process
parameters such as pressure duration, squeeze pressure,
and pouring and die temperatures as outputs.
3.6 BP algorithm tuned NN
A detailed parametric study is conducted to determine
the optimum network parameters for better predictions.
The result of the parametric study is presented in
Tab le 5. It should be noted that after the network pa-
rameters are optimized, 15 test cases were passed in
batch mode to the optimized NN to obtain the process
parameters. The BPNN training completed with the
mean squared error of 0.022292. Further, the average
Fig. 5 Models comparison for predicting the combined responses in
terms of average absolute percent deviation (Forward mapping)
Tabl e 5 BPNN parametric study results of reverse mappings
Neural network parameters Optimum network parameter values
Hidden neurons 23
Learning rate-hidden layer, η0.6775
Learning rate-output layer, η0.455
Momentum constant, α0.455
Activation constant-hidden layer 7.3
Activation constant-output layer 5.5
Bias 0.0000505
Tabl e 6 GA-NN parametric study results of reverse mappings
GA-NN parameters Optimum parameter values
Mutation probability 0.0001515
Population size 260
Generations number 510
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absolute percent deviation in prediction of combined
responses is found to be equal to 5.18 %.
3.7 GA tuned NN
The input parameters (process variables) and outputs
(casting properties) of forward mapping are treated as
the outputs and inputs, respectively, in reverse map-
ping. GA parameters are optimized after conducting a
detailed parametric study, and the obtained results are
presented in Table 6. The GA-NN training ends with
the mean squared error of 0.022632, and the average
absolute PD in predictions of all the network outputs
is found equal to 5.46 %.
Fig. 6 Model comparison in terms of PD in prediction apressure duration and bsqueeze pressure
Fig. 7 Model comparison in terms of PD in prediction apouring temperature and bdie temperature
Tabl e 7 Models comparison for
predicting the process parameters
(reverse mapping)
Process parameters Average absolute deviation in prediction (%)
BPNN GA-NN
Pressure duration 7.33 6.67
Squeeze pressure 6.49 7.14
Pouring temperature 1.76 1.76
Die temperature 5.13 6.26
Average of all process parameters 5.18 5.46
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3.8 Comparison of reverse mappings of neural network
models
Fifteen random test case results while predicting the
process parameters via revere mappings by utilizing
the neural network (BPNN and GA-NN) models are
discussed below,
The BPNN and GA-NN model for pressure duration predic-
tion in terms of percent deviation is shown in Fig. 6a.ThePD
predictionvaluesarefoundtovaryintherangeof−13.96 to
14.39 % for BPNN and −6.62 to 12.16 % for GA-NN models.
Figure 6b shows the plot representing the BPNN and
GA-NN models prediction of squeeze pressure in terms
of PD. It is noteworthy that neural (BPNN and GA-NN)
models yielded similar trend in PD in prediction.
However, BPNN showed slightly better performance
thanGA-NN.ThePDinpredictionisseentovaryin
the levels of −23.03 to 12.17 % for BPNN and −23.89
to 12.66 % for GA-NN model (refer to Fig. 6b).
Figure 7a compares the BPNN and GA-NN models
prediction performance in terms of PD for the pouring
temperature. The plot indicates that both models follow
a similar pattern; however, GA-NN has shown slightly
better performance as compared to BPNN. Moreover,
the PD in the prediction of pouring temperature is
foundtobelyingintherangeof−4.36 to 2.55 % for
BPNN and −4.01 to 2.5 % for GA-NN.
Figure 7b represents the plot of PD in prediction for
die temperature NN models. It is worth noting that the
BPNN prediction performance is found to be better than
GA-NN towards this response. Furthermore, the PD in
prediction of die temperature using neural models is
found to fall in the range of −12.24 to 11.42 % for
BPNN and −17.48 to 11.77 % for GA-NN.
3.9 Comparison of the models
Tab le 7compares the average absolute percent deviation
in prediction of the individual and the combined re-
sponses of BPNN and GA-NN models in reverse map-
ping. The percent deviation from the zero line showed
larger deviation for both models as compared to forward
prediction. This might be due to the fact that in most of
the manufacturing processes, the behaviour of the re-
sponses varies non-linearly with respect to the indepen-
dent variables. Increase of one parameter and decrease
of the other and vice versa may result in a similar
output effect. Thus, the neural network model perfor-
mances are considered as data dependent. The results
have shown that the BPNN model is found to make
better prediction than GA-NN in most of the cases.
The reason might be due to adaptability of the model
to capture complex non-linearity in the process and er-
ror surface. Thus, it can be concluded that the evolu-
tionaryGAtunedNNperformsbetteronlywhentheBP
algorithm tuned NN get trapped in local minima.
However, the practical requirements in predicting the
process parameters can be effectively tackled using neu-
ral network based approaches via reverse mapping.
Although both models are capable of making effective
reverse mapping predictions, BPNN is the finally pre-
ferred one due to a better average absolute PD in pre-
diction (considering all responses) as shown in Fig. 8.
4Conclusions
The neural network-based approaches have been used to
carry out the input-output modelling of the squeeze
casting process in both forward and reverse directions.
The batch mode training requires huge data sets which
are generated artificially through the regression equa-
tions. The following conclusions are drawn from the
present study:
1. In the present work, different responses are mea-
sured on the same casting specimen. It is notewor-
thy that all responses need to be estimated simulta-
neously, or else interdependency among the outputs
(if any) might be lost. Since the analysis is carried
out response wise, conventional regression analysis
Fig. 8 NN models comparison in terms of PD in prediction considering
all process parameters (reverse mapping)
Int J Adv Manuf Technol

approach might fail to capture the interdependency
among the responses. Neural networks are capable
of predicting multi-outputs simultaneously, resulting
in integral approach.
2. In forward mapping, the quality characteristics (i.e.
yield strength, surface roughness and ultimate tensile
strength) are predicted for the known set of process
variables (i.e. pressure duration, squeeze pressure,
pouring temperature and die temperature). The
BPNN, GA-NN and statistical models prediction
performances have been compared for 15 test cases.
Although the neural network approaches are trained
with the data collected from the regression models,
the results have shown that GA-NN slightly
outperformed the other models while predicting the
responses, surface roughness and yield strength.
Furthermore, the non-linear regression models
outperformed neural network models in prediction
of ultimate tensile strength. Moreover, GA-NN re-
sults are comparable with the non-linear regression
based CCD model in predicting the responses. The
average absolute deviation in prediction in terms of
percentage obtained for the combined responses
using different models is found equal to 4.87 %
for BPNN, 3.54 % for GA-NN, 3.54 % for CCD
and4.32%BBD,respectively.
3. By utilizing the neural network-based approaches,
the process parameters for the desired quality can
be obtained. Furthermore, the performances of the
neural network models have been compared among
themselves by utilizing 15 test cases. It is interesting
to note that BPNN outperformed GA-NN in
predicting most of the responses. The overall perfor-
mance of BPNN is slightly better as compared to
GA-NN. The reason might be the fact that the na-
ture of error surface. BPNN results are found to be
better for uni-modal error surfaces. The grand aver-
age absolute percent deviation in prediction of com-
bined process variables is found equal to 5.18 % for
BPNNand5.46%forGA-NN.
4. The NN-based approaches are capable of making effec-
tive forward and reverse mapping predictions. The reverse
mapping predictions are more useful for a foundry man in
online monitoring of the process. Furthermore, reverse
mapping also helps to reduce the cost incurred in the
selection of the most influential process parameters, ma-
terial wastages, energy consumption, and casting simula-
tion software.
Acknowledgments The authors greatly acknowledge the Dept. of
Applied Mechanics and Hydraulics, National Institute of Technology
Karnataka, India, for their kind support in carrying out the experiments.
Appendix I
Tabl e 8 Summary of input-output results of the test cases
Exp. no. Squeeze cast process variables Responses
A B C D SR/R
a
(μm) UTS, MPa YS, MPa
1 36 96 682 211 0.73 194 126
2 41 57 646 231 1.02 178 117
3 33 55 661 213 1.08 180 116
4 27 69 692 203 0.94 188 114
5 35 54 677 215 0.98 183 114
6 42 117 684 230 0.46 213 138
7 42 106 673 251 0.53 207 135
8 29 61 707 232 0.92 188 116
9 32 68 680 256 0.74 191 121
10 38 114 642 241 0.55 208 136
11 39 105 663 213 0.56 206 135
12 36 55 684 202 1.08 180 116
13 33 43 685 163 1.33 179 116
14 28 44 712 199 1.25 177 108
15 34 41 702 203 1.16 178 112
Int J Adv Manuf Technol

Back propagation neural network
Declare network failure
End
Error goal
Reached?
Exceed Max.
I
te
r
at
i
o
n
?
Save weights
Load test cases
Predict
network results
Generate input-output training data
through response equations
An integrate system development
to co-relate in
p
ut and out
p
uts
Initialize random weights, network
p
arameters
,
error
g
oal and trainin
g
e
p
ochs
Forward calculation to estimate network output
Load training data via batch mode
Determine error by comparing
network output and target values
Backward calculation to u
p
date s
y
na
p
tic wei
g
hts
End of e
p
och
I = I +1
Yes
N
o
N
o
Yes
Examine ex
p
erimental needs
Define objective(s)
Identify control and noise
factors influencing response(s)
Determine the controllable
variable ranges of a process
Select particular design of experiments
and design the experimental matrix
Perform experiments as per design and collect
experimental data with three replicates
Establish either linear or non-linear input-output
relationships usin
g
software
Analyze the collected data to estimate the performances
Significance and
ANOVA test
Estimate individual, combined
effect on the responses
Test the developed model
performances with random test cases
Start
Appendix II
Flow chart illustrating methodology followed in squeeze casting process modelling via DOE based BPNN
Int J Adv Manuf Technol

No
Y
es
No
Yes
GA String =
GA String + 1
Assign fitness
to all strin
g
s
Re
p
roduction
Cross over
Mutation
Gen. = Gen+1
Case=
Case+1
Start
case=0
Case> max
Case
Determine output
usin
g
NN
Calculate
fitness of
a string
GA
string
=0
GA string
>Pop
GA
Starts
Initial Population
Generation = 0
End
Gen >
Max gen
No
Y
es
Appendix III
Steps followed in GA-NN modelling [29]
Int J Adv Manuf Technol

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