3. 1 CHAPTER-3 ARTIFICIAL NEURAL NETWORK AND NEURO-FUZZY MODELLING OF HOT EXTRUSION PROCESS,EQUAL CHANNEL ANGULAR PRESSING, ORTHOGONAL CUTTING PROCESS AND END MILLING PROCESS 3.1 Introduction ntelligent Manufacturing Systems (IMS) are manufacturing systems that are able to respond to rapid changes in designs and demand, without the intervention of the humans. To respond to the changing demand scenarios the system must be equipped with a comprehensive manufacturing planning and control system which incorporates vast amounts of manufacturing knowledge in a form that is accessible rapidly. The design and implementation of these systems is one of the major challenges facing the manufacturing engineer today. As already discussed in chapter-1 and chapter-2, metal forming process is characterised by a multiplicity of dynamically interacting process variables, usually too complicated and are not amenable to analytical models. The advent of domain specific finite element (FE) codes like FORGE 3 to handle large deformation plasticity has made accurate analysis possible. The basic limitations of FE modelling are code development, debugging, pre-processing and program execution which consume a lot of time. Though FEM provides a basis for forging optimisation, but a small change in a single process parameter requires a new forging simulation run to predict its effects on quality of forging as well as on final forging load. Because the potentially viable processing routes are numerous, many FEM process simulations are necessary to identify the required process variables. Some researchers tried to apply simplex algorithm [Kus89], genetic algorithm [Dug94, Roy97], and novel computational methods [ChenMF95, Fou96a, Fou96b, Gel98, Lor00, Har01] for optimisation of forging process but this required a large number of process simulations to find a satisfactory solution. Therefore, a need is felt to develop a much more generalised model, which can predict the final result for a wide variation in I
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3. 1
CHAPTER-3
ARTIFICIAL NEURAL NETWORK AND NEURO-FUZZY MODELLING OF
HOT EXTRUSION PROCESS, EQUAL CHANNEL ANGULAR PRESSING,
ORTHOGONAL CUTTING PROCESS AND END MILLING PROCESS
3.1 Introduction
ntelligent Manufacturing Systems (IMS) are manufacturing systems that are able to
respond to rapid changes in designs and demand, without the intervention of the
humans. To respond to the changing demand scenarios the system must be equipped
with a comprehensive manufacturing planning and control system which incorporates
vast amounts of manufacturing knowledge in a form that is accessible rapidly. The
design and implementation of these systems is one of the major challenges facing the
manufacturing engineer today.
As already discussed in chapter-1 and chapter-2, metal forming process is
characterised by a multiplicity of dynamically interacting process variables, usually
too complicated and are not amenable to analytical models. The advent of domain
specific finite element (FE) codes like FORGE 3 to handle large deformation
plasticity has made accurate analysis possible. The basic limitations of FE modelling
are code development, debugging, pre-processing and program execution which
consume a lot of time. Though FEM provides a basis for forging optimisation, but a
small change in a single process parameter requires a new forging simulation run to
predict its effects on quality of forging as well as on final forging load. Because the
potentially viable processing routes are numerous, many FEM process simulations are
necessary to identify the required process variables. Some researchers tried to apply
simplex algorithm [Kus89], genetic algorithm [Dug94, Roy97], and novel
computational methods [ChenMF95, Fou96a, Fou96b, Gel98, Lor00, Har01] for
optimisation of forging process but this required a large number of process
simulations to find a satisfactory solution. Therefore, a need is felt to develop a much
more generalised model, which can predict the final result for a wide variation in
I
Chapter-3
3. 2
process parameters quickly without resorting to extensive numerical simulations for a
given design.
To meet this demand two novel approaches i.e. Artificial Neural Network (ANN) and
Neuro Fuzzy (NF) techniques are used for modelling;
Hot extrusion process to predict the forging force required to complete the
process,
Equal Channel Angular Pressing (ECAP) to predict average equivalent strain
induced and the required forming energy,
Orthogonal cutting process to predict cutting forces for a given set of input
parameters i.e. speed, feed and depth of cut and
End milling process to predict average surface roughness and machining time.
The NF models of hot extrusion process and ECAP are developed out of training data
obtained from the Finite Element (FE) simulations detailed in chapter-2. This work
has considerable implications in selection and control of process variables in real time
and ability to achieve energy and material savings with quality improvement and is a
step towards intelligent manufacturing.
3.2 Artificial Neural Networks (ANN)
Artificial Neural networks (ANN) are systems that try to make use of some of the
known or expected organizing principles of the human brain. ANN’s most prominent
feature is to learn from examples, and then adapt themselves based on actual solution
space (training data sets) [Fau94, Hay94, Roj93]. ANN consists of a number of
independent, simple processors - the neurons. These neurons communicate with each
other via weighted connections. Learning in neural networks means to determine a
mapping from an input to an output space by using example patterns. If the same or
similar input patterns are presented to the network after learning, it should produce an
appropriate output pattern. They are particularly powerful in clustering the solution
space identifying important features [Tic00]. ANN can be used if training data is
available. It is not necessary to have a mathematical model of the problem of interest.
On the other hand ANN’s are sometimes criticized for being opaque i.e. the
knowledge they represent is stored in a non-readable form. The solution obtained
from the learning process of ANN is usually cannot be interpreted. They cannot be
Chapter-3
3. 3
checked whether their solution is plausible, i.e. their final state cannot be interpreted
in terms of rules. The learning process itself can take very long, and there is usually
no guarantee of success.
In this work Back-Propagation learning methodology with Levenberg -Marquardt
(LM) approximation is adopted for supervised learning of the networks and is briefly
described below:
The Back-Propagation (BP) neural network is a multiple layer network with one input
layer, one output layer and some hidden layers between input and output layers
[Fau94]. Its learning procedure is based on gradient search with least sum squared
optimality criterion. Calculation of the gradient is done by partial derivative of sum
squared error with respect to weights. This algorithm can be expressed succinctly in
the form of a pseudo-code as given below.
1. Pick a rate parameter R.2. For each sample input compute the resulting output until performance is
satisfactory 3. Compute (error)for nodes in the output layer using;
D Oz z z where D represents the desired output and O represents the actual output of the
neuron.4. Compute β for all other nodes using;
1W O Oj k j k k k k 5. Compute weight changes for all weights using;
1w rO O Oi j i j j j 6. Add up the weight changes for all sample inputs and change the weights.
The standard BP algorithm suffers from the serious drawbacks of slow convergence
and inability to avoid local minima. Therefore, BP with Levenberg -Marquardt (LM)
approximation is used in this work. LM learning rule uses an approximation of the
Newton's method to get better performance [Mor77]. This technique is relatively
faster but requires more memory. The LM update rule is:
1T TW J J I J e
Where J is the Jacobean matrix of derivatives of each error to each weight, is a
scalar and e is an error vector. If the scalar is very large, the above expression
approximates the Gradient Descent method while when it is small the above
Chapter-3
3. 4
expression becomes the Gauss - Newton method. The Gauss Newton method is faster
and more accurate near error minima. Hence, the aim is to shift towards the Gauss -
Newton as quickly as possible. The is decreased after each successful step and
increased only when the step increases the error.
3.3Neuro-fuzzy systems
3.3.1 Fuzzy Systems
Fuzzy logic was founded by Lofti A. Zadeh in 1965 [Zad65]. Fuzzy systems have
been developed to manage knowledge in a more natural manner. It is based on the
idea that sets are not crisp but some are fuzzy, and these can be modeled in linguistic
human terms such as large, small and medium. In fuzzy systems, rules can be
formulated that use these linguistic expressions, which allows integration of domain
expertise into model synthesis and apply them to the human behavioral problem.
Using fuzzy set theory it is easy to model the ‘fuzzy’ boundaries of linguistic terms by
introducing gradual memberships. Interpretations of membership degrees include
similarity, preference, and uncertainty [Dub96]. In general, due to their closeness to
human reasoning, solutions obtained using fuzzy approaches are easy to understand
and to apply. Due to these strengths, fuzzy systems are the methods of choice, if
linguistic, vague, or imprecise information has to be modeled [Kru99]. A fuzzy
system can be used to solve a problem if knowledge about the solution is available in
the form of linguistic if-then rules. By defining suitable fuzzy sets to represent
linguistic terms used within the rules, a fuzzy system can be created from these rules.
There is no formal model of the problem of interest and no training data required. On
the other hand fuzzy systems are mathematically opaque which makes conventional
analysis and exploitation of empirical data hard to perform.
3.3.2 Neuro-Fuzzy systems
Combinations of neural networks with fuzzy systems called as NF systems where
both models complement each other. Neuro-fuzzy systems allow to overcome some of
the individual (ANN and Fuzzy systems) weaknesses and offer some appealing
features. Neuro-Fuzzy hybrid systems combine the advantages of fuzzy systems,
which deal with explicit knowledge which can be explained and understood, and
neural networks which deal with implicit knowledge which can be acquired by
learning [Jan95, Von95, Jin00, Ang03, Abr05]. The ANN is used to define the
Chapter-3
3. 5
clustering in the solution space which results in creation of the fuzzy sets. The ANN
learns these clusters based on actual human behavior test data. A further advantage is
that the solution space rather than being represented point by point as some expert
systems “clumps’ the space as described by Kosko [Kos92]. This results in fewer
rules and lower computer resources and thus reduces design time and cost. On the
other hand, fuzzy logic enhances the generalization capability of a neural network
system by providing more reliable output when extrapolation is needed beyond the
limits of the training data [Lin96]. Neural networks and Fuzzy logic have some
common features such as distributed representation of knowledge, model-free
estimation, ability to handle data with uncertainty and imprecision. Fuzzy logic has
tolerance for imprecision of data, while neural networks have tolerance for noisy data
[Nau97].
A NF system is trained by a learning algorithm (usually) derived from neural network
theory. The (heuristic) learning procedure operates on local information, and causes
only local modifications in the underlying fuzzy system. The learning process is not
knowledge based, but data driven. A NF system can be viewed as a special multi-
layer feed-forward neural network. The first layer represents input variables, the
middle (hidden) layer(s) represents fuzzy rules and the last layer represents output
variables. Fuzzy sets are encoded as (fuzzy) connection weights. A NF system can
always (i.e. before, during and after learning) be interpreted as a system of fuzzy
rules. It is both possible to create the system out of training data from scratch, and it is
possible to initialize it by prior knowledge in the form of fuzzy rules. Modern NF
systems are usually represented as multilayer feed forward neural networks [Ber92,
Buc94, Buc92, Hal94, Nau96a, Nau96b]. In NF models, connection weights and
propagation and activation functions differ from common neural networks.
The NF system is capable of extracting fuzzy knowledge from numerical data and
linguistic data into the system. The goal here is to avoid difficulties encountered in
applying fuzzy logic for systems represented by numerical knowledge (data sets), or
in applying neural networks for a system presented by linguistic information (fuzzy
sets). Neither fuzzy reasoning systems nor neural networks are by themselves capable
of solving problems involving at the same time both linguistic and numerical
knowledge [Hal94]. A number of researchers have used the term hybrid systems
Chapter-3
3. 6
[Ful00] to depict systems that involve in some ways both fuzzy logic and neural
networks features.
A NF system approximates an n-dimensional (unknown) function that is partially
given by the training data. It is possible to view a fuzzy system as a special neural
network and to apply on a learning algorithm directly (hybrid models).
3.4 Artificial Neural Network (ANN) modelling of hot extrusion process
In this section, the ANN modelling of hot extrusion is described. The data obtained
from the FEM simulations in FORGE3 environment of hot extrusion process in
chapter-2, table 2.3 is used to train the ANN model. This model is used to predict the
extrusion load for given parameter combinations of hot extrusion in real-time without
having to perform any extensive and costly computations. For modelling hot extrusion
process a three layer network with three inputs i.e. die angle, coefficient of friction,
and initial temperature of billet and single output i.e. extrusion load is designed as
shown in figure 3.1. After training, the weights are frozen and the model is validated.
For this purpose, the input parameters to the network are sets of values that have not
been used for training the network but are in the same range as those used for training.
Fig. 3.1: Three input and one output ANN architecture of hot extrusion process
Chapter-3
3. 7
Validation enables us to test the network with regard to its capability for interpolation.
The extrusion load is thus obtained for specified set of parameters. Then an FE
simulation is performed for the same sets of parameters to determine the extrusion
load through the FE simulation. The level of agreement between the forging force
predicted by the neural network and the FE simulation indicates the efficacy of the
neural model.
For this training problem the following parameters were found to give rapid
convergence of the training network with good performance in the estimation;
First and second layers of neurons are modelled with log of sigmoid function,
and the third layer is purely linear function. Neurons taken in first and second
layers are eight (8) and five (5) respectively.
Maximum epochs considered are 1000, error goal is set to 10-8 and learning
rate for training the network is taken as 0.2.
Comparison between FE simulation results/training data and neural network results is
shown in table 3.1. The results of the validation procedure described above are given
in table 3.2. The close agreement of the values of the equivalent strain and forming
energy obtained by the neural network and the FE simulation clearly indicates that the
model can be used for predicting the extrusion force in the range of parameters under
consideration. Convergence graphs between sum squared error and number of epochs
for training process is shown in Fig. 3.2. It can be clearly seen that neural network
training got completed in just ninety four (94) epochs with the above mentioned
parameters.
The proposed ANN model is very fast and the time taken for prediction is very small.
This meta model can be used in tandem with optimizer in future for finding the
optimal hot extrusion process parameters for minimizing extrusion force.
Chapter-3
3. 8
Fig. 3.2: Convergence graph between sum squared error and number of epochs for hot extrusion process
Angle μ
FE simulation values and NN estimated values of Extrusion load (Tones) 1000oC 1090oC 1180oC 1260oC
Table 3.12: FE simulation results and NF estimated results for extrusion load of hot extrusion process
Chapter-3
3. 25
Fig. 3.10: Initial and final membership functions for the NF model of hot extrusion process
Number of nodes: 78Number of linear parameters: 108Number of nonlinear parameters: 27Total number of parameters: 135Number of training data pairs: 60Number of checking data pairs: 30Number of fuzzy rules: 27
Table 3.13: Training information of NF model for hot extrusion process
Validation of neuro-fuzzy model for hot extrusion process: After developing the
NF model from training it by FE simulation data the model is validated. For this, the
input parameters to the NF model are sets of values that have not been used for
training the model but are in the same range as those used for training. This enables us
to test the network with regard to its capability for interpolation. The final extrusion
force is thus obtained for this set of parameters. Then an FE simulation is performed
for the same sets of parameters to determine the extrusion force. The level of
agreement between the extrusion force predicted by NF model and the FE simulation
indicates the conformity of the NF model. The results of the validation procedure
described above are given in table 3.14. The close agreement of the values of the final
extrusion force obtained by the NF model and the FE simulation clearly indicates that
Chapter-3
3. 26
the model can be used for predicting the extrusion force in the range of parameters
under consideration. The model is very fast and prediction can be done in real time.
Table 3.16: Training data and NF estimated results for forming energy(kJ) of ECAP process
Chapter-3
3. 33
Number of nodes: 35Number of linear parameters: 27Number of nonlinear parameters: 18Total number of parameters: 45Number of training data pairs: 63Number of checking data pairs: 31Number of fuzzy rules: 9
Table 3.17: Training parameters of NF architecture for ECAP process
Fig. 3.14: Initial and final membership functions for the NF model of ECAP process
Validation of neuro-fuzzy model for ECAP process: After developing the NF
model from training it by FE simulation data the model is validated. For this, the input
parameters to the NF model are sets of values that have not been used for training the
model but are in the same range as those used for training. This enables us to test the
network with regard to its capability for interpolation. The final extrusion force is thus
obtained for this set of parameters. Then an FE simulation is performed for the same
sets of parameters to determine the extrusion force. The level of agreement between
the extrusion force predicted by NF model and the FE simulation indicates the
conformity of the NF model. The results of the validation procedure described above
are given in table 3.18. The close agreement of the values of the average equivalent
strain and forming energy obtained by the NF model and the FE simulation clearly
indicates that the model can be used for predicting these output parameters in the
range of parameters under consideration. The model is very fast and prediction can be
Table 3.19: Experimental and estimated values of cutting forces for speed, feed and depth of cut
Chapter-3
3. 37
The results of the validation procedure are given in table 3.20. The close agreement of
the values obtained by the experimental values reported by Nagaraju et al. and
predicted values by NF model clearly indicates that the model can be used for
predicting the output in the range of parameters under consideration. Training
parameters and initial and final membership functions of NF model for cutting forces
(Fc & Ft) are shown in table 3.21 and figure 3.16.
Speed(m/min)
Feed(mm)
Depthof
Cut(mm)
Exp. Valuesof Cutting
Forces [Nag97]Values byNF Model
Fc (N) Ft (N) Fc (N) Ft (N)22 0.212 1.0 419.0 257.1 419 257.029 0.440 1.2 714.3 476.2 714 476.213 0.212 1.2 571.4 380.9 571.2 380.817 0.107 1.5 380.9 238.1 380.9 238.0
Table 3.20: Validation of estimated values of cutting forces using NF model with experimental values reported by Nagaraju et al.
Number of nodes: 78Number of linear parameters: 108Number of nonlinear parameters: 27Total number of parameters: 135Number of training data pairs: 32Number of checking data pairs: 16Number of fuzzy rules: 27
Table 3.21: Training parameters of NF architecture for orthogonal cutting
process (Fc & Ft)
Fig. 3.16: Initial and final membership functions of orthogonal cutting forces(Fc & Ft)
Chapter-3
3. 38
3.10 Neuro-Fuzzy modelling of end milling process
The data obtained from the mentioned experimental setup in table 3.8, section 3.5 is
used to train the NF model for end milling process. The NF model is developed on
similar pattern as developed for forming processes in section 3.7 and 3.8. Neuro-fuzzy
inference system under consideration has four inputs as shown in figures 3.17 and
3.18 viz. cutting speed, feed rate, radial depth of cut, tolerance and one output
machining time and average surface roughness. The overall output is expressed as
linear combinations of the consequent parameters. The output f can be rewritten as
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181
( ) ( ) ( ) ( ) ( )1
f w fi ii
f w p w q w r w s w ti i i i ii i i i ii
This is linear in the consequent parameters. The forward pass of the learning
algorithm continues up to nodes at layer 4 and consequent parameters are determined
by the method of least squares. In the backward pass, the error signal propagates
backward to update the premise parameters by gradient descent.
Fig. 3.17: A four input and one output (machining time) neuro-fuzzy network model for end milling
Chapter-3
3. 39
Fig. 3.18: A four input and one output (average surface roughness) neuro-fuzzy network model for end milling
The experimental values reported by Tansel et al. [Tan06] and the computed values
after training NF model are listed in table 3.22. The close agreement of the values
obtained by the model and those reported by Tansel et al., [Tan06] clearly indicates
that the model can be used for predicting the values in the range of parameters under
consideration. The model is very fast and the time taken for prediction is negligible.
machining time using NF model with experimental values
Number of nodes: 193Number of linear parameters: 405Number of nonlinear parameters: 36Total number of parameters: 441Number of training data pairs: 81Number of checking data pairs: 40Number of fuzzy rules: 81
Table 3.24: Training Parameters of NF architecture for end milling process
Fig. 3.19: Initial and final membership functions for the NF model of end millingprocess
Chapter-3
3. 42
3.11 Statistical Regression Modelling
Regression modelling is a statistical tool for the investigation of relationships between
two or more variables. It establishes the relationship between a dependent variable or
response that depends upon one or more independent variables. In this section
statistical regression models for hot extrusion process, ECAP, orthogonal cutting
process and end milling process are developed and are compared with NF models,
discussed in the previous sections. A brief introduction of regression model is as
follows:
Regression modelling is used when two or more variables are thought to be
systematically connected by a linear relationship. Suppose we wish to develop an
empirical model relating a single dependent variable or response ‘y’ to the two
independent or regressor variables x1 and x2. A model that might describe this
relationship is:
0 1 1 2 2y x x
Above equation is a linear regression model with two independent variables, where
0 , 1 and 2 are unknown parameters. The model describes a plane in the two
dimensional x1, x2 space. The parameter 0 defines the intercept of the plane and
parameters 1 and 2 are called regression coefficients. The is the error term.
The regression model fitting in this work is done using a statistical software package
known as MINITAB 15. It can be used for learning about statistics as well as
statistical research. Statistical analysis computer applications have the advantage of
being accurate, reliable, and generally faster than computing statistics and drawing
graphs by hand. Minitab is user friendly and is relatively easy to use.
In order to judge the accuracy of the regression prediction model, relative percentage
error ϕ and average relative percentage error ϕa are used which are defined as:
100%FE V
FE
P E
P
Chapter-3
3. 43
1
n
ia
n
where PFE is predicted finite element simulation value , EV is estimated value of the
model and n is the number of observations.
3.11.1 Regression modelling of hot extrusion process
Statistical regression model is developed using Minitab 15 for hot extrusion process
and is compared with NF model and FE model. Through the regression analysis of
the results, the values of the model coefficients have been obtained and the regression
equation for extrusion load as response is given as under: