Modeling properties drive elements of cars after heat treatment
processes by means of neural networks
Michal Szota and Jozef Jasinski
Czestochowa University of Technology,
Faculty of Materials Processing Technology and Applied Physics,
Materials Engineering Institute,
Biomaterials and Surface Layer Research Institute,
Av. Armii Krajowej 19, 42-200 Czestochowa, Poland
e-mail address: [email protected]
ABSTRACT
This paper presents the possibility of using neural networks model for designing
carbonizing process in fluidized bed. This process is very complicated and difficult as
multi-parameters changes are non-linear and car drive cross structure is non
homogeneous. This fact and lack of mathematical algorithms describing this process
makes modeling properties of drives elements by traditional numerical methods difficult
or even impossible. In this case it is possible to try using artificial neural network. The
neural network structure is designed and specially prepared by choosing input and
output parameters of the process. The method of learning and testing of a neural
network, the way of limiting nets structure and minimizing learning and testing error are
discussed. Such prepared neural network model, after putting expected values of car
cross driving properties in output layer, can give answers to a lot of questions about
running carbonizing process in fluidized bed. The practical implications of the neural
network models are the possibility of using them to build control system capable of online controlling running process and supporting engineering decision in real time. The
originality of this research is a different concept to obtain expected materials properties
after carbonizing in fluidized bed. The specially prepared neural networks model could
be a help for engineering decisions and may be used in designing carbonizing process
in fluidized bed as well as in controlling changes during this process
Keywords
Applications, neural networks modeling, artificial intelligence, materials engineering.
Introduction
The carbonizing process in fluidized bed is multi-parameters and complex [1,2],
because changes of parameters during this process have non linear characteristic,
shown in Fig. 1. The next problem is the lack of mathematical algorithms that could
describe it. Using neural networks for modeling carbonizing in fluidized bed is caused by
several nets features:
-
non linear character,
ability to generalize the results of calculations for data out of training set,
no need for mathematical algorithms describing influence changes input
parameters on modeling materials properties [3-7].
The research is divided into six stages:
-
choosing modeling properties of materials,
choosing heat treatment parameters to building data input vector,
using a special computer system to obtain a training data set,
designing and building a neural network structure,
minimizing a model structure, training and testing error,
practical verification of calculation results.
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At present different carbonizing techniques are used in the thermo-chemical
treatment. One of this is carbonizing in fluidized bed. This is characterized by high
coefficient heat and mass transfer. These techniques are very often used in research
institutes and small industrial plants [1,8,9].
Research equipment
This research are has been carried out in Biomaterials and Surface Layer
Research Institute of Czestochowa University of Technology. This institute administers
a special computer system, which is used for visualization and control of thermal and
thermo-chemical treatment in fluidized bed [9-11]. This system enables high precision in
gas medium dosage. Gas distribution station is used for controlling fife different gases
flows, which is shown in Fig. 2.
Fig. 2 Gas distribution station PGIMP-1 [11].
This station is controlled by a special computer system. This system is composed
of one PC computer using Windows NT operation system and InTouch 7.1 software,
whose main interface is shown in Fig. 3. It is connected with GE Fanuc drivers system,
which are connected with the gas distribution station and used for gas dosage.
Fig. 3 Main interface menu of visualization system [11]
This computer system make it possible to obtain information about running of
carbonizing processes. In further research data obtained in this way is used to build
a data input vector. The data input vector is useful for training and testing neural
network, which is built in an artificial neural network simulator. “Statistyka” and
“Neuronix” software are useful building an artificial neural network.
Materials for research
Material for this research ha been provided by Visteon Industrial plant, which
produces car drive crosses used in a lot of car models. The main problem in car drive
cross properties designed is non homogeneous metallographic structure in car drive
cross provided to Visteon, which is presented in fig. 4, 5.
3
2
1
Fig. 4 cross-section macrostructure of a fry etched car drive cross with visible fluid lines in, scale
1:1
Non homogeneous metallographic structure in car drive cross causes difficulty in
designing carbonizing process, because it is very hart to obtain the same properties of
a carbonized layer in all material’s parts.
Work methodology
Modeling the process using by neural networks can be started with designing the
structure of the network. The characteristic features of neural nets are the following: the
number of layers, the number of neurons in each layer and kinds of neural connections.
The number of neurons an in input layer and the number of input parameters are
usually equal. For carbonizing steel process in a fluidized bed n = 13. Neural networks
input is described by the following variables parameters:
x1 - tPod heating time,
x2 – tA austenitizing time,
x3 – tCh³ cooling time,
x4 – tOdp tempering time,
x5 – TWej temperature of batch,
x6 – TA austenitizing temperature,
x7 – TCh³ cooling temperature,
x8 – TOdp tempering temperature,
x9 – kind of atmosphere,
x10 – ap air excess ratio,
x11 – kind of cooling,
x12 – lenght of batch,
x13 – width of batch.
The size of output layer is equal with number of searched parameters. For car
driving crosses is possible modeling for example thickness of carbon surface layer,
surface hardness in characteristic places and microhardness schedule in surface layer.
In this case number of neurons in output layer equals eight:
y1–microhardness in the depth 10?
mm after carbonizing treatment,
y2–microhardness in the depth 50?
mm after carbonizing treatment,
y3–microhardness in the depth 100?
mm after carbonizing treatment,
y4–microhardness in the depth 150?
mm after carbonizing treatment,
y5–microhardness in the depth 200?
mm after carbonizing treatment,
y6–microhardness in the depth 250mm after carbonizing treatment,
y7–thickness of carbon surface layer,
y8–surface hardness in characteristic places.
After fixing the input and the output layer structure the next step is designing the
inside layers of the model. As mathematic algorithms describing correlations between
vectors xn and yk are not known it is necessary to use an unconventional way of building
the neural nets. It is based on information about output and input.
Theoretically the problem of choosing neural structure is restricted to approximation of
multi-variable function for given vector xn [3]. The case discussed in this paper concerns
multi-dimensional input vector and continuous activation function. Building that kind of
neural network model is defined by Kolmogorow statement [12]. He proved that in order
to obtain k-dimensional output vector yk for n-dimensional input
vector xn and continuous activation function, using one hidden layer neural
network built of 2n+1 neurons is sufficient. It is shown in fig. 6.
1
Z1
X1
Y1
X2
Y8
X 13
Z27
Fig. 6 Structure of neural network for modeling hardness in accordance with
Ko³mogorow statement.
Where :
x=[x1,x2,...,xn] – n – dimensional input vector,
y=[y1,y2,...,yk] – k – dimensional output vector,
z1,z2,....,z2n+1 – hidden layer neurons.
Kolmogorow didn’t define activation function algorithm, because it is chosen for a
particular process likewise the number of hidden layers which changes in range from n
to 3n.
In order to use the designed neural network in practice it should be taught by
learning data set. The size of learning data set depends on the expected generalization
degree, which is the correct answer of model for the input data different from the data of
learning set. Neural networks taught by learning set are far bigger than the number of
adapted parameters of network ( the quantity of synaptic weights connecting artificial
neurons ) would have better generalized qualities. If those proportions are disturbed, the
network has reproduction abilities. In order to obtain the best approximation qualities for
a designed model it is necessary to minimize the number of adapted parameters of
network and, in consequence, minimize EG(w) - generalization error (1):
æp
ö
EG (w ) £ E L (w )+ e ç , E L ÷
(1)
èh
ø
where:
EL – learning error (2),
e?
?- range of trust,
h - the number of all synaptic weights.
p
E L (w ) = å E (yk (w ), d k )
(2)
k =1
When the generalization error increases, the model becomes interpolator for
which all input signals, different from those of the training set are rejected as a measure
background. In order to avoid that it is necessary to minimize the generalization error by
means of either building bigger training set or limiting the network structure. However
limiting the network structure excessive cause the increase of learning error EL(w),
which similarly to EG(w) when it goes from maximum to minimum. Before it reaches
minimum EG(w) starts behaving in the other way (it increases in contrast to decreasing
EL(w)). This quality can be used in searching minimum EG(w), because it could make
the selection of network structure faster. Direct observation of EG(w) is very timeconsuming, because searching its minimum needs checking error EG(w) for fully learned
network each time. A better solution is observing error EL(w), which changes can be
observed continuously during teaching the network. In this case the structure of
networks could be corrected each time after stopping teaching process with the
constant control value of learning set, because too big a learning set causes the reincrease the generalization error.
Description of results of a own research
250
250
200
150
100
predermined hardness
c a l c u l ah
t ea sr d n e s s
0
5
7
2
0
2
2
0
8
1
0
4
1
0
1
8
1
5
0
0
5
3
5
0
5
7
2
0
2
2
0
8
1
0
4
1
0
1
8
1
5
0
0
5
3
5
2
27
0
22
5
14
0
80
11
0
50
35
20
18
0
calculated hardnes s
100
0
0
d i st a n ce o n t he s u rf a c e um
predetermined hardness
150
50
50
distance on the surface um
200
2
H ard n ess H V
100
50
0
h arn ess H V
300
250
200
150
5
Hardness, HV
The method proposed in the paper makes to possible obtain assumed curve of a
car drives cross hardness after carbonizing process in fluidized bed, which is build with
eight approximated point. This eight point is different for places shown in the fig. 5.4.
Fig. 7.1-7.3 present comparison of the required curve of car driving cross hardness after
carbonizing process with the curves calculated.
d i st a n ce o n t he s u rf a c e um
p r e d e r t in e d h a r d n e s s
c a l c u l a theadr d n e s s
Fig. 7.1-7.3 - Comparison of the assumed and calculated curve of hardness for place 1
shown in fig. 5.4 (7.1- in paces 1, 7.2 – in place 2, 7.3 – in place 3)
Two last output neurons delivers information of surface hardness and thickness of layer.
Conclusions
The following conclusions are down from this work:
- Such prepared a neural network model, after putting expected values of modeling
properties in output layer, can give answers to a lot of questions about running
carbonizing process in a fluidized bed.
- The information obtained in this way can be used in practice by engineering
designed running carbonizing process and property of final products.
- This research will be continued to complex solve this subject and applied it in
a industrial plant. The final solution will be special computer system, which will be
connected in real time [13] with heat medium and gas distribution station. This
connection and a special work application make to possible to add new date in
a training and testing data.
- Connection of this system whit heat treatment control system makes to possible online control running process [14-15] and support engineering decision in real time.
Acknowledgment
This research was carried out with the financial support of Polish State Committee for Scientific
Researches under Grant No. 3565/T02/2006/31.
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