# Intelligent Control of the Complex Technology Process Based on Adaptive Pattern Clustering and Feature Map

Authors: Wushan Cheng
Journal: Mathematical Problems in Engineering
 (2008)

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## Abstract

A kind of fuzzy neural networks (FNNs) based on adaptive pattern clustering and feature map (APCFM) is proposed to improve the property of the large delay and time varying of the sintering process. By using the density clustering and learning vector quantization (LVQ), the sintering process is divided automatically into subclasses which have similar clustering center and labeled fitting number. Then these labeled subclass samples are
taken into fuzzy neural network (FNN) to be trained; this network is used
to solve the prediction problem of the burning through point (BTP). Using the 707 groups of actual training process data and the FNN to train APCFM algorithm, experiments prove that the system
has stronger robustness and wide generality in clustering analysis and feature extraction.


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## Body

## 1. Introduction

Sintering
is the most widely  used agglomeration  process for
iron ores  and is a very
important chain of iron making. In general, the process of sintering includes
three major phases. First, it involves blending all the ores thoroughly according
to certain proportions and adding water to the ore mix to produce particles.
Second, the actual sintering operation is initiated by the ignition of the
cokes as the raw mix passes under gas ignition. Finally, after traveling the
length of the strand, the finished sinter is broken up, cooled, and screened
[1, 2].
In the recent twenty years, many methods of integrity and fusion have been
explored by the metallurgy and automation experts.


### 1.1. Mathematical Model

According to the chemical/physical characteristics for
sintering, a model was formulated as a series of differential equations to
describe the relation between the thick martial, the
ignition temperature, and the bellows temperature at the tail of the
machine. For the time varying and randomness of the sintering process, many mechanisms have still
not been understood. Although the dynamic model is tenable at a certain
boundary condition, it is difficult to cover the whole process.


### 1.2. Neural Network-Based Model

For the fast approach of
neural network, a model can be established rapidly from the given input and
output data, and it can also solve the problem of this long-time
delay system. In general, genetic algorithm is used to optimize the parameters of
the network and improve the generalization of the system, but it has still not
been reported to be used in real-time control.


### 1.3. Rule-Based Model

The  rule base,
acknowledge, database,
and inference machine can be constructed by the technology and operation experts’ experience
[3].
Rule base and inference machine are mainly used in estimating the process,
analyzing cause, and deciding guideline. Acknowledge includes operation data, fact,
mathematical model, and elicitation and unit
knowledge. Database stores real-time data from production and equipment.
Unfortunately, most results of this model are still simulation results.


## 1.1. Mathematical Model

According to the chemical/physical characteristics for
sintering, a model was formulated as a series of differential equations to
describe the relation between the thick martial, the
ignition temperature, and the bellows temperature at the tail of the
machine. For the time varying and randomness of the sintering process, many mechanisms have still
not been understood. Although the dynamic model is tenable at a certain
boundary condition, it is difficult to cover the whole process.


## 1.2. Neural Network-Based Model

For the fast approach of
neural network, a model can be established rapidly from the given input and
output data, and it can also solve the problem of this long-time
delay system. In general, genetic algorithm is used to optimize the parameters of
the network and improve the generalization of the system, but it has still not
been reported to be used in real-time control.


## 1.3. Rule-Based Model

The  rule base,
acknowledge, database,
and inference machine can be constructed by the technology and operation experts’ experience
[3].
Rule base and inference machine are mainly used in estimating the process,
analyzing cause, and deciding guideline. Acknowledge includes operation data, fact,
mathematical model, and elicitation and unit
knowledge. Database stores real-time data from production and equipment.
Unfortunately, most results of this model are still simulation results.


## 2. Fuzzy Neural Network

In general, the dynamic behavior of a fuzzy logical
controller is characterized by a set of linguistic control rules based on the knowledge
of an expert [4].Consider the fuzzy controller with Gaussian MFs and multiplication
implication; the topology structure of fuzzy  neural network is shown in
Figure1.Figure 1
The topology
structure of fuzzy neural network.The fuzzy rule is as follows:(2.1)R(l):ifxi=Fil,xn=Fnl,    then (2.2)y=Gil. The input and output
relationship is shown as(2.3)f(x)=∑l=1My¯l(∏i=1nμFil(xi))∑l=1M(∏i=1nμFil(xi)), where x=(x1,x2,…,xn)T is the system input, M the is rule number, n is the input
number, μFil(xi) is the membership function in the input xi=Fil, and y¯l is the value when the membership function equals the maximum in l rule. The fuzzy neural network
[4] has five-layer structure.The first
layer is input variable layer. In this layer, theith inputs are represented as xi;
the system can have n inputs.The second
layer is membership layer. In this layer, each node performs the Gaussian function;
the function is adopted as a membership function. The membership function of the
input is defined as(2.4)μFil(xi)=exp[−(xi−x¯ilσil)2], where x¯il is the Gauss meaning of the rule input xi,
and σil is the square error.The third layer is rule layer. The layer is used to
implement the antecedent matching. The matching operation or the fuzzy and
aggregation operation is chosen as the simple product operation. In this layer,
summing is finished by neuron.In addition toy¯l between the third and the fouth layers, other layer
weights equal 1.The
fifth layer is output of the fuzzy neural network.Thus,
the entire fuzzy neural network
[5] needs to adjust x¯il,σil,y¯l     parameters to control the process. These parameters
have specified signification; therefore, they are initialed by language
information in order to improve learning convergence speed.


## 3. Adaptive Pattern Clustering and Feature Map Network

### 3.1. Initial Data Space Clustering

According to technology character and
equipment requirement, density sintering speed and burning temperature are
selected as input vectors; the temperature and pressure of 18 windboxes and the waste
gas temperature are chosen as output vectors. The input space scatter diagram
is obtained by using the input sample to do three-vector space map, and the
clustering centerCij(i=1,2,3;j=1,2,…,ki) and subspace
[aj,bj]
of every vector are found by
utilizing feature extract based on density clustering. These rectangle areas
are intersected with each other to form
k=k1×k2×k3
subregions.


### 3.2. Feature Map

Feature map network  developed by
Kohonen is an unsupervised competitive learning cluster network in which only
one neuron is on at any time. The map is an artificial system that emulates the
brain in the visual system, and which includes three major phases
[5–7].Competitive
phase: the inputs of the network can be written as vector byX=[x1,x2,…,xm]T, and
the synaptic weight
vector of neuron j in the two-dimensional (2D)
array is given by wj=[wj1,wj2,…,wjm]T,j=1,2,…,l,
where m is the
local number of output neurons in the 2D
array and l is the total number of
the neurons of network. In order to find the best match of input vector x with
the synaptic weight wj, the multiplication
wjTx determined the center location of the exciting
neuron’s topology neighborhood and the maximum of wjTx is equal to the Euclid  norm in mathematics.Cooperative
phase: the winner neuron is
located in the center of the cooperation neuron’s topology neighborhood.
We supposed thathji
is
the topology neighborhood whose
center is the victory neuron i, and
dij
is the inclination
distance between victory neuron i and excited
neuron j. A classical selection of
hji
to satisfy these
conditions is (3.1)hji=exp(−dji22σ2), where σ is the effective width of topology
neighborhood. The trend of topology neighborhood is shown in
Figure 2.Figure 2
The
trend of topology neighborhood coast line.Self-adjusting phase: it includes self-ordering and
converging stages; self-ordering formula is(3.2)wj(n+1)=wj(n)+η(t)hj,i(x)(n)(x(n)−wj(n)),η(n)=η0exp(−nτ).The  equation
is in converging stage; learning rateη(n) is made smaller gradually.


### 3.3. Learning Vector Quantification

The
learning vector
quantification (LVQ) algorithm is used to adjust fine weight vector to improve
quality in decision area by utilizing supervisor learning skill. The foundation
method is first to find the average value of the attribute of
every subclass on the
basis of clustering, second to make a comparison
between the average value of the subclass and the whole
vector, and last to label the up-arrowhead tag with the larger values and the
down-arrowhead with the smaller values. The set of every labeled
subclasses may be expressed as the
direction of its weight shifting. For this purpose, let theLxi
stand for the tag of the input
vector xi, and let
Lwj
stand
for the tag of the weight
wj; the recursive function
is defined as follows.IfLwj=Lxi, then(3.3)wj(n+1)=wj(n)+αn(xi−wj(n)). If Lwj≠Lxi, then(3.4)wj(n+1)=wj(n)−αn(xi−wj(n)), where 0<αn<1.Passing
through a period of time iteratively, the subclasses with the same property may
be converged together, and the other subclasses with different properties may be
departed from each other.In this paper, we use the actual data as the samples
from sintering process. The input vectors are density, velocity, and ignition
temperature, and the output vectors are the temperature and pressure of 18 windboxes and
the temperature of waste gas.


## 3.1. Initial Data Space Clustering

According to technology character and
equipment requirement, density sintering speed and burning temperature are
selected as input vectors; the temperature and pressure of 18 windboxes and the waste
gas temperature are chosen as output vectors. The input space scatter diagram
is obtained by using the input sample to do three-vector space map, and the
clustering centerCij(i=1,2,3;j=1,2,…,ki) and subspace
[aj,bj]
of every vector are found by
utilizing feature extract based on density clustering. These rectangle areas
are intersected with each other to form
k=k1×k2×k3
subregions.


## 3.2. Feature Map

Feature map network  developed by
Kohonen is an unsupervised competitive learning cluster network in which only
one neuron is on at any time. The map is an artificial system that emulates the
brain in the visual system, and which includes three major phases
[5–7].Competitive
phase: the inputs of the network can be written as vector byX=[x1,x2,…,xm]T, and
the synaptic weight
vector of neuron j in the two-dimensional (2D)
array is given by wj=[wj1,wj2,…,wjm]T,j=1,2,…,l,
where m is the
local number of output neurons in the 2D
array and l is the total number of
the neurons of network. In order to find the best match of input vector x with
the synaptic weight wj, the multiplication
wjTx determined the center location of the exciting
neuron’s topology neighborhood and the maximum of wjTx is equal to the Euclid  norm in mathematics.Cooperative
phase: the winner neuron is
located in the center of the cooperation neuron’s topology neighborhood.
We supposed thathji
is
the topology neighborhood whose
center is the victory neuron i, and
dij
is the inclination
distance between victory neuron i and excited
neuron j. A classical selection of
hji
to satisfy these
conditions is (3.1)hji=exp(−dji22σ2), where σ is the effective width of topology
neighborhood. The trend of topology neighborhood is shown in
Figure 2.Figure 2
The
trend of topology neighborhood coast line.Self-adjusting phase: it includes self-ordering and
converging stages; self-ordering formula is(3.2)wj(n+1)=wj(n)+η(t)hj,i(x)(n)(x(n)−wj(n)),η(n)=η0exp(−nτ).The  equation
is in converging stage; learning rateη(n) is made smaller gradually.


## 3.3. Learning Vector Quantification

The
learning vector
quantification (LVQ) algorithm is used to adjust fine weight vector to improve
quality in decision area by utilizing supervisor learning skill. The foundation
method is first to find the average value of the attribute of
every subclass on the
basis of clustering, second to make a comparison
between the average value of the subclass and the whole
vector, and last to label the up-arrowhead tag with the larger values and the
down-arrowhead with the smaller values. The set of every labeled
subclasses may be expressed as the
direction of its weight shifting. For this purpose, let theLxi
stand for the tag of the input
vector xi, and let
Lwj
stand
for the tag of the weight
wj; the recursive function
is defined as follows.IfLwj=Lxi, then(3.3)wj(n+1)=wj(n)+αn(xi−wj(n)). If Lwj≠Lxi, then(3.4)wj(n+1)=wj(n)−αn(xi−wj(n)), where 0<αn<1.Passing
through a period of time iteratively, the subclasses with the same property may
be converged together, and the other subclasses with different properties may be
departed from each other.In this paper, we use the actual data as the samples
from sintering process. The input vectors are density, velocity, and ignition
temperature, and the output vectors are the temperature and pressure of 18 windboxes and
the temperature of waste gas.


## 4. Experiment

### 4.1. Analysis of the Input in Three-Dimensional Space

The distributing diagram of the two-year input samples
in three-dimensional space is shown in Figure3. We can obtain 12 subspaces by
using the initialization clustering of the samples, which is based on the
density of the samples, and maps the feature of 12 subspaces to form the topology
structure, which is shown in Figure 4, and the center of every subspace is
dotted in Figure 3.Figure 3
The distributing diagram of samples.Figure 4
The
topology structure of clustering.


### 4.2. Analysis of the Input Samples’ Classification

Computing
the  average value of every property for each subclass, respectively, such as
density (D), velocity
(V), and ignition temperature
(T), and comparing the
average value of the
subclass property with the property of the whole samples, if the result of a
subclass is bigger than the average value of the whole samples, we use up-arrowhead
marking; otherwise we use down-arrowhead marking. The marking classification is
listed in Table 1.Table 1
The setting of subclass property.
SubclassNumDVTCompare results1650.66430.79860.8039D↓V↑T↑2290.66590.78930.6781D↓V↑T↓3400.64620.72080.3900D↓V↑T↓4920.70390.77790.8215D↑V↑T↑5170.64710.67750.6662D↓V↑T↓6320.61490.59210.5671D↓V↓T↓7950.75490.75050.8696D↑V↑T↑8270.69870.67710.8178D↑V↑T↑9960.60670.51840.7202D↓V↓T↓10750.75580.68920.8749D↑V↑T↑11340.64680.53610.7817D↓V↓T↑121050.59930.45570.7410D↓V↓T↓In this table, we can find 5 different large classes.
Row 1 is a class, rows 2, 3, 5 are a class, rows 4, 7, 8, 10 are a class, rows
6, 9, 12 are a class, and row 11 is a class.
Figure5 shows the relations
between the topology structure and the class table.(a) The results of fuzzy neural
network training (FNN). (b) The results of adaptive pattern
clustering and feature map (APCFM).
(a)(b)According
to the characters of process and performance of equipments, we can get the property
of each class in Figure4.Class
1 (D↓V↑T↑). The samples of class denote the thick stuffing of sinter bed, high ignition
temperature, and fast velocity, and it may cause
raw ore.Class
2 (D↓V↑T↓). It denotes the thick stuffing of sinter  bed, low ignition temperature,
and fast velocity, and it causes easily raw ore, and the burning through point
will be back to the strand tail.Class
3 (D↑V↑T↑). The class denotes loose stuffing on the sinter bed, high ignition
temperature, and fast velocity, and it causes easily sintering for sintering
process.Class
4 (D↓V↓T↓). The phenomenon shows the thick stuffing on the sinter bed, low ignition
temperature, and slow velocity, and it is in accordance with the thick and slow
sintering.Class 5 (D↓V↓T↑). This state denotes the thick stuffing of sinter bed, high ignition
temperature, and slow velocity, and we should direct our attention to the
sinter bed earlier in order to avoid the  oversintering.


### 4.3. Learning Vector Quantization

According
to the analysis above, 12 subclasses have been readjusted into 5 classes. Now,
retraining the whole input samples by using the LVQ network, the network is a
characteristic studying of having teacher. The
training network with the LVQ can improve the hitting accuracy of feature map
that is proved by [6]. The network output can get the tag of the class
when it  enters the sample through  the network. We show the step as follows. List
the input vectors P, the output vectors
T, and the class of classificatory  tag
C: (4.1)P=[0.75607,0.81711,0.78968,0.6468,…,0.75626;0.67327,0.66337,0.64356,0.5361,…,0.68317;0.96873,0.92471,0.95533,0.7817,…,0.95406;],T=[1245⋯3],C=[1000⋯00100⋯00000⋯10010⋯00001⋯0].


### 4.4. Training Every Subclass Sample by Using Fuzzy Neural Network

The
testing results are shown in Figures5(a) and
5(b); Figure 5(a) is only genetic
neural network testing results, and Figure 5(b) is the testing results by using
the adaptive pattern clustering and feature map FNN. We compare the two figures
and find out that FNN can obtain the trend of network output, but the precision
is low. The adaptive pattern clustering and feature mapFNN can improve a high precision for network output and have a
good generalization for the samples which belong to the same class.


## 4.1. Analysis of the Input in Three-Dimensional Space

The distributing diagram of the two-year input samples
in three-dimensional space is shown in Figure3. We can obtain 12 subspaces by
using the initialization clustering of the samples, which is based on the
density of the samples, and maps the feature of 12 subspaces to form the topology
structure, which is shown in Figure 4, and the center of every subspace is
dotted in Figure 3.Figure 3
The distributing diagram of samples.Figure 4
The
topology structure of clustering.


## 4.2. Analysis of the Input Samples’ Classification

Computing
the  average value of every property for each subclass, respectively, such as
density (D), velocity
(V), and ignition temperature
(T), and comparing the
average value of the
subclass property with the property of the whole samples, if the result of a
subclass is bigger than the average value of the whole samples, we use up-arrowhead
marking; otherwise we use down-arrowhead marking. The marking classification is
listed in Table 1.Table 1
The setting of subclass property.
SubclassNumDVTCompare results1650.66430.79860.8039D↓V↑T↑2290.66590.78930.6781D↓V↑T↓3400.64620.72080.3900D↓V↑T↓4920.70390.77790.8215D↑V↑T↑5170.64710.67750.6662D↓V↑T↓6320.61490.59210.5671D↓V↓T↓7950.75490.75050.8696D↑V↑T↑8270.69870.67710.8178D↑V↑T↑9960.60670.51840.7202D↓V↓T↓10750.75580.68920.8749D↑V↑T↑11340.64680.53610.7817D↓V↓T↑121050.59930.45570.7410D↓V↓T↓In this table, we can find 5 different large classes.
Row 1 is a class, rows 2, 3, 5 are a class, rows 4, 7, 8, 10 are a class, rows
6, 9, 12 are a class, and row 11 is a class.
Figure5 shows the relations
between the topology structure and the class table.(a) The results of fuzzy neural
network training (FNN). (b) The results of adaptive pattern
clustering and feature map (APCFM).
(a)(b)According
to the characters of process and performance of equipments, we can get the property
of each class in Figure4.Class
1 (D↓V↑T↑). The samples of class denote the thick stuffing of sinter bed, high ignition
temperature, and fast velocity, and it may cause
raw ore.Class
2 (D↓V↑T↓). It denotes the thick stuffing of sinter  bed, low ignition temperature,
and fast velocity, and it causes easily raw ore, and the burning through point
will be back to the strand tail.Class
3 (D↑V↑T↑). The class denotes loose stuffing on the sinter bed, high ignition
temperature, and fast velocity, and it causes easily sintering for sintering
process.Class
4 (D↓V↓T↓). The phenomenon shows the thick stuffing on the sinter bed, low ignition
temperature, and slow velocity, and it is in accordance with the thick and slow
sintering.Class 5 (D↓V↓T↑). This state denotes the thick stuffing of sinter bed, high ignition
temperature, and slow velocity, and we should direct our attention to the
sinter bed earlier in order to avoid the  oversintering.


## 4.3. Learning Vector Quantization

According
to the analysis above, 12 subclasses have been readjusted into 5 classes. Now,
retraining the whole input samples by using the LVQ network, the network is a
characteristic studying of having teacher. The
training network with the LVQ can improve the hitting accuracy of feature map
that is proved by [6]. The network output can get the tag of the class
when it  enters the sample through  the network. We show the step as follows. List
the input vectors P, the output vectors
T, and the class of classificatory  tag
C: (4.1)P=[0.75607,0.81711,0.78968,0.6468,…,0.75626;0.67327,0.66337,0.64356,0.5361,…,0.68317;0.96873,0.92471,0.95533,0.7817,…,0.95406;],T=[1245⋯3],C=[1000⋯00100⋯00000⋯10010⋯00001⋯0].


## 4.4. Training Every Subclass Sample by Using Fuzzy Neural Network

The
testing results are shown in Figures5(a) and
5(b); Figure 5(a) is only genetic
neural network testing results, and Figure 5(b) is the testing results by using
the adaptive pattern clustering and feature map FNN. We compare the two figures
and find out that FNN can obtain the trend of network output, but the precision
is low. The adaptive pattern clustering and feature mapFNN can improve a high precision for network output and have a
good generalization for the samples which belong to the same class.


## 5. Conclusion

In this paper, in order to predict the BTP, an
APCFM reference and FNN system have
been proposed to solve the challenging problem of the sinter production
process, which is a typical nonlinear, time-varying, and multimode process, and
is very difficult to solve using traditional methods. In our approach, a
density clustering is used to determine the number of the initial input vectors
consciously, and a feature map algorithm is used to extract data relevance
property from different subclasses and improve the confidence of the vector. By using the
teacher’s instruction, LQV network can herd effectively feature categories together on
this basis FNN algorithm. The constructed system has been trained with input
sample consisting of 707 technology
groups and measuring apparatus of two-year actual process and has obtained very
good performance; especially, comparing APCFM+FNN with FNN
[8, 9],
the precision of training and testing has raised one time and three times,
respectively, and the running time decreases more than one time, and it is satisfied with the demand
of real time running and improving the robustness of the system.



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*Source: 783278-2008-10-08.xml*