Mei C., Zhou J., Peng X. Simulation and Optimization of Furnaces and Kilns for Nonferrous Metallurgical Engineering
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4 Thermal Engineering Processes Simulation Based on Artificial Intelligence
Fig. 4.2 Flow chart of identification algorithm for fuzzy adaptive decision-making model
4.3.2
Example: fuzzy adaptive decision-making model for nickel
matte smelting process in submerged arc furnace
If the slow-varying factors in a smelting process are neglected, the furnace can be
considered as a multi-variable system as shown in Fig. 4.3. Sulfide nickel calcine is
the most important raw material, quartzite is used as slag-making flux, coke powder
is used as reducer, while, liquid hot converter slag is partially inputted to the electric
furnace in order to increase the yield of nickel and cobalt. The produced slag is
abandoned after breaking up by water, flue gas is sent to dust collection workshop,
and low-nickel matte is sent to converter for converting.
Xiaoqi Peng and Yanpo Song
Fig. 4.3
Submerged arc furnace
The characteristics of the process mentioned above is as follows:
a) Composition of raw materials is complex and unsteady.
b) It is difficult to realize real-time and accurate measurement of the
technology parameters such as materials’ composition, temperature and so on.
c) There exists serious random disturbances.
d) Decision-making and operation rely on human experiences.
e) Production indexes fluctuate acutely.
4.3.2.1
Modeling approach
The production indexes are influenced by many factors, such as the strong
coupling among various parameters, the complex thermodynamic and dynamic
problems, energy conversion problems and so on. All these factors influence one
another in such a complex way that the smelting system in smelter is typical
complex system with multi-variable, nonlinearity, long time-delay and so on.
Therefore, only if the integrated balance point of all factors can be found out, it
can be possible to realize the overall optimization of smelting process and
achieve the goal of energy saving and consumption reducing.
Traditionally, decision making of smelting a process relies on a material and
heat balance model. This model plays an important role in guiding production,
but it is not suitable for dynamic real production process because it is essentially
static. Besides, there are big error and long time delay measurements because of
the faultiness of measurement instruments, which limit the application of material
and heat balance model. Therefore, in real production worksite, operation control
mainly relies on human experience; production process is influenced seriously by
human factors; smelter condition is not enough steady; techno-economical
indexes and production indexes fluctuates acutely.
The main controllable variables of a smelting process are input of nickel
calcine, flux and converter slag, electric power of furnace, output of low-nickel
matte and slag. Although the operating voltage is changeable in production, it
4 Thermal Engineering Processes Simulation Based on Artificial Intelligence
keeps constant under normal production conditions, so it is not regarded as a
controllable variable in this chapter.
If the composition and optimal input of calcine were estimated by some
algorithm, then the optimal input of flux and producer could be estimated
according to the furnace condition, composition and input of calcine, and then the
optimal smelting power of electric furnace could be estimated according to the
furnace condition and input of materials. Finally, the optimal output of low nickel
matte and slag could be decided according to the estimated results mentioned
above and the furnace condition. Thus, the integrated index of production process
would be optimized, and the goal of energy saving and consumption reducing
would be achieved. To realize these, an optimization decision-making model is
necessary.
Nickel smelter is a complex system with the characteristics of multi-variable,
nonlinear and long time delay. It is difficult to build a precise mathematical
model based on smelting mechanism, but the experienced spot workers and
technicians can ensure the safety of a production process depending on their
abundant experience. Fuzzy model has strong ability to approach a complex
system with the characteristics of multi-variable, nonlinear and long time delay,
and can describe human strategy of operation and control by way of language,
while the huge amount of real production data accumulated in production practice
contains human experience. Therefore, if the human experience was extracted
from the data by using the strong ability of computer in data processing and
computing, and expressed as fuzzy decision-making rules in the form of “If …
and … Then …”, then these rules constitute the fuzzy decision-making model for
a smelting process. If new decision-making rules were generalized constantly in a
production process, that is, the model was revised constantly so that it would
have good adaptability.
Based on the above analysis
ˈit is proposed to build an adaptive fuzzy decision
model for a smelting process(Peng,1998;Mei et al.,1994a,b) using the methods
introduced in Section 4.3.1 and taking energy saving and consumption reducing
as our goal.
Composition of calcine is unstable and its measure data delays about two shifts,
for different types of calcine, different decision-making models are need to obtain
control variables. Therefore, we classify calcine according to its percentage
contents of Fe, SiO
2
and S firstly, then build a fuzzy optimization
decision-making model for each type. Before making a decision, forecast the
composition of the inputting calcine, then classify the calcine using the fuzzy
clustering method(Li,1986), finally, finish the optimal decision-making for the
production process using the corresponding model.
Xiaoqi Peng and Yanpo Song
4.3.2.2
Objective function and optimal data
The wastage functions of the melting process in a smelting furnace was defined
as
zn n
bb
b
yzd
Qdw
x
=+
••
•
(4.19)
where d
b
is the price of electric energy (yuan/kW• h);
b
w is the electric energy
consumption per ton of calcine (kW
• h/t); y
z
is the output of the smelting slag
(t/shift); z
n
is the percentage content of nickel slag (%); d
n
is the price of nickel
(yuan/t); x
b
is the weight of the calcine inputted per shift (t/shift); Q is the
wastage function of the melting process in a submerged arc furnace for nickel
matte.
The value of Q reflects synthetically the value of energy consumed and nickel
lost, data with small value Q are selected as optimal data, a fuzzy model based on
optimal data is the fuzzy optimization decision making model.
4.3.2.3
Calcine composition forecasting model
Percentage contents of Fe, SiO
2
and S in calcine are unsteady, while measurement
data delay several shifts in general, so it is necessary to forecast the composition
of calcine, therefore, it is proposed to build calcine composition forecasting
autoregressive model (AR model) as follows(Peng et al.,1993):
a) Iron content in calcine,
)()3()2()1()(
FeFeFe3FeFe2FeFe1Fe
kekbckbckbckb +−+−+−= (4.20)
b) SiO
2
content in calcine,
)()3()2()1()(
SiSiSi3SiSi2SiSi1Si
kekbckbckbckb +−+−+−= (4.21)
c) Sulfur content in calcine,
S 1SS 2SS 3SS S
() ( 1) ( 2) ( 3) ()bk cbk cbk cbk ek=−+−+−+ (4.22)
where b
Fe
(k) is iron content of calcine inputted in the kth shift; e
Fe
(k) is iron
content forecast error of the kth shift; b
Si
(k) is SiO
2
content of calcine inputted in
the kth shift; e
Si
(k) is SiO
2
content forecast error of the kth shift; b
S
(k) is sulfur
content of calcine inputted in the kth shift; e
S
(k) is sulfur content forecast error of
the kth shift.
The value of parameters should minimize error square sum, that is, the follows
should be satisfied:
min)(
4
2
Fe
→
∑
=
N
k
ke min)(
4
2
Si
→
∑
=
N
k
ke min)(
4
2
S
→
∑
=
N
k
ke
Therefore, given N (N
ı6) groups of calcine composition data, the parameters
of AR model can be obtained by means of the least squares method. To ensure the
accuracy of forecasting result, the model parameters should be revised according
new valid data before forecasting, that is, make the forecasting model can reflect
4 Thermal Engineering Processes Simulation Based on Artificial Intelligence
duly the change of calcine composition.
4.3.2.4
Fuzzy adaptive decision-making model for production process in
submerged arc furnace
According to mechanism analysis of smelting process, considering of operation
and control experience of spot technicians, and through stepwise regression
analyzing the huge amount of real production data accumulated in production
practice, the following relation functions can be obtained:
a) Input of calcine at time k:
),2(),1(),2(),1(),2(),1([)(
WWSSbbbb
−−−−−−= kxkxkxkxkxkxFkx
)]2(),1(),2(),1(),2(),1(
zzddff
−−−−−− kykykykykxkx (4.23)
b) Input of converter slag at time k:
),2(),1(),2(),1(),2(),1(),([)(
WWSSbbbff
−−−−−−= kxkxkxkxkxkxkxFkx
)]2(),1(),2(),1(),2(),1(
zzddff
−−−−−− kykykykykxkx (4.24)
c) Input of quartz sand at time k:
SSbb b S S
WW fff
dd zz
( ) [ ( ), ( 1), ( 2), ( 1), ( 2),
( 1), ( 2),(),( 1),( 2),
( 1), ( 2), ( 1), ( 2)]
xk Fxkxk xk xk xk
x k x k xkxk xk
yk yk yk yk
=−−−−
−− −−
−− −−
(4.25)
d) Electric energy consumption at time k:
WWbb b SS
SWWff
fddzz
( ) [ ( ), ( 1), ( 2), ( ), ( 1),
( 2), ( 1), ( 2), ( ), ( 1),
( 2), ( 1), ( 2), ( 1), ( 2)]
x k F xkxk xk xkxk
xk xk xk xkxk
xk yk yk yk yk
=−−−
−−− −
−−−−−
(4.26)
e) Input of coke powder at time k:
)]1(),(),1(),([)(
ffbbcc
−−= kxkxkxkxFkx
(4.27)
f) Output of low nickel matte at time k:
ddbb b WW W
ff d d d
( ) [ ( ), ( 1), ( 2), ( ), ( 1), ( 2),
(),( 1),( 1),( 2)]
Δ ()
yk Fxkxk xk x kx k x k
xkxk yk yk yk
=−− −−
−−−+
(4.28)
g) Output of slag at time k:
zzbb b SS
SWWWf
fzz z
( ) [ ( ), ( 1), ( 2), ( ), ( 1),
( 2), ( ), ( 1), ( 2), ( ),
(1),(1),(2)]
Δ ()
yk Fxkxk xk xkxk
xk xkxk xk xk
xk yk yk yk
=−−−
−−−
−−−+
(4.29)
where,
⎪
⎩
⎪
⎨
⎧
−
<<
−
=Δ
)İ(/)(
)(0
)ı(/)(
)(
lll
hl
hlh
d
LLkLL
LLL
LLkLL
ky
(4.30)
⎪
⎩
⎪
⎨
⎧
−
<<
−
=Δ
)İ(/)(
)(0
)ı(/)(
)(
lzl
hl
hzh
z
ZZkZZ
ZZZ
ZZkZZ
ky
(4.31)
Xiaoqi Peng and Yanpo Song
where L is the height of liquid matte surface; L
h
is the max allowable height of
liquid matte surface; k
l
is correction coefficient for the height of liquid matte
surface; L
l
is the minimum allowable height of liquid matte surface; Z is the
height of liquid slag surface; Z
h
is the maximum allowable height of liquid slag
surface; k
z
is correction coefficient for the height of liquid slag surface; Z
l
is the
minimum allowable height of liquid slag surface;
)(
d
kyΔ is called matte
surface height correction coefficient;
)(
z
kyΔ
is called slag surface height
correction coefficient.
According to Eq. 4.23 through Eq. 4.29 and the method introduced in Section
4.3.1, the fuzzy adaptive decision-making model for a smelting process can be
built, the process of decision-making based on this model can be shown as Fig.
4.4.
Fig. 4.4 Fuzzy decision-making process of submerged arc furnace
4.4
Modeling Based on Fuzzy Neural Network Analysis
For complex industrial systems that haven’t sufficient samples, it is difficult to
develop optimal decision model directly using methods introduced in Section 4.3.
In such a case, fuzzy neural network adaptive modeling methods are more
suitable for multi-variable system. In this section, an optimal decision model for
4 Thermal Engineering Processes Simulation Based on Artificial Intelligence
slag cleaning arc furnace is developed with this modeling method.
4.4.1
Fuzzy neural network adaptive modeling methods of
multi-variable system
Providing a system with r inputs )(tx
i
(i=1,2,…,r) and q outputs )(ty
j
(j=1, 2, …,
q), the value of any input
)(kx
i
at time k is decided by Eq. 4.7:
12
12
1
11 1
() ()
L
TT Tl
l
i Ll
LL L
l
ll l
ll l
xk ek
λ
λλ
λ
λλ λ
K
=
== =
=+++ +
∑
∑∑ ∑
ϕ θ ϕ θ ϕ θ
(4.32)
According to Eq. 4.3 through Eq. 4.5 and Eq. 4.32, a fuzzy neural network (Peng
et al., 1995) can be constructed as Fig.4.5, where
, ě, ģ, h, / represent
calculating the membership function value, summating, minimizing,
multiplication, division for corresponding neuron, respectively.
4.4.1.1
Identification of fuzzy neural network decision making model of multi-
variable system
The learning algorithm of fuzzy neural network is inferred as follows.
Rewriting Eq. 4.32 as:
11 2 2
1
1
1
() [ ] ()
L
TT T l
iLLl
L
l
l
l
xk ek
λλ λ λ
λ
K
=
=
=++++
∑
∑
θ ϕ θ ϕ θ ϕ
12 1 2
1
1
1
[][ ] ()
L
TT TT l
LLl
L
l
l
l
ek
λλ λ ϕ λ
λ
KK
=
=
=+
∑
∑
θ θ θ
(4.33)
Let
12
'[ ]
TT TT
L
LΘ =
θ θ θ
(4.34)
Then
11 1 1 1 1 1 1
011 1 111 1 1
22 2 2 2 2 2 2
011 1 111 1 1
011 1 111 1 1
'
rn mqqm
rn mqqm
LL L L L L L L
rn mqqm
aa a a b b b b
aa a a b b b b
aa a ab b b b
KK KKK
KK KKK
MMMMMM
KK KKK
Θ
⎡⎤
⎢⎥
⎢⎥
⎢⎥
=
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
(4.35)
Let error function J be
2
)]()(
ˆ
[
2
1
kxkxJ
ii
−=
(4.36)
where
)(
ˆ
kx
i
is the practical input in an optimal sample and
)(kx
i
is the output
calculated by the fuzzy neural network. The study target of the fuzzy neural
network is to minimize J.
According to one order gradient algorithm:
Xiaoqi Peng and Yanpo Song
00
1
()
ˆ
[() ()]
()
il
ii
L
ll
i
l
l
xk
JJ
xk xk
axka
λ
λ
=
∂
∂∂
==−−
∂∂ ∂
∑
•• (4.37)
''
1
()
ˆ
[() ()] ( ')
()
il
ii i
L
ll
ii i ii
l
l
xk
JJ
xk xk xk i
axka
λ
λ
=
∂
∂∂
==−− −
∂∂ ∂
∑
••• (4.38)
''
1
()
ˆ
[() ()] ( ')
()
il
ii j
L
ll
jj i jj
l
l
xk
JJ
xk xk
y
k
j
bxkb
λ
λ
=
∂
∂∂
==−− −
∂∂ ∂
∑
••• (4.39)
where, i
Ą=1, 2, …, n; jĄ=1, 2, …, m.
Let
ˆ
() () ()
iii
xk xk xkΔ= − (4.40)
12
[]
T
l
λλ λ
= K
λ
(4.41)
Then, according to Eq.4.37 through Eq.4.39, we have:
00
1
()
T
i
L
l
l
xk
η
λ
λ
=
Δ
′′
′′
=+Δ=+
∑
•
••
ΘΘ ΘΘ
ϕ
(4.42)
where
η
is the learning speed of the neural network;
0
Θ
is the original value of
Θ .
Equation 4.42 is the learning algorithm of the neural network, it also can be
regarded as an identification algorithm for a fuzzy decision-making and control
model. The fuzzy neural network can be trained with optimal samples; the
trained neural network is an optimal decision-making and control model; the
decisions made by this model are optimal decisions; the control executed by it
is optimal control.
In order to simplify network structure and accelerate the learning process,
firstly, n and m should be decided by a structure identification method on the
basic of mechanism analysis and practical operation control experiences; then,
the input or output variables with weaker effect should be ignored by some
analysis; finally, the network with structure as shown in Fig. 4.5 can be
decided.
4.4.1.2
Fuzzy adaptive algorithm
Slowly-varying of external environments, production conditions and the system
structure can lead to the decline of the performance of decision-making model. To
make the model have the capability of self-learning and self-adaptation, new
optimal samples produced in real production should be used to “update” the
neural network, that is, the decision-making model is revised dynamically to cater
for current situation of the system and store new optimal decision-making
experiences. Therefore, the decision-making ability of the model is improved
increasingly.
4 Thermal Engineering Processes Simulation Based on Artificial Intelligence
Fig. 4.5 Fuzzy neural network control model of multi-variable system
4.4.1.3
Convergence of neural network
The major problems existing in modeling process are how to improve the
convergence speed of a learning process and how to judge the learning result is
global optimal or not. To accelerate the learning process, learning speed
η
is
fuzzy adjusted: when error is big, a big
η
is used to accelerate the learning speed;
while, when error is small, a small
η
is used to improve the approximation
accuracy of the neural network. By this method, the learning process is accelerated.
There is no mathematical method to judge whether the result is global optimal or
not, so it is judged directly by practice: performing the real time simulation to the
production process using a trained neural network model; if the simulation result is
accurate, the model is considered as optimal model.
Xiaoqi Peng and Yanpo Song
4.4.2
Example: fuzzy neural network adaptive decision-making
model for production process in slag cleaning furnace
If the slow-varying factors in slag a cleaning process are neglected, the furnace can be
thought as a multi-variable system as shown in Fig. 4.6. Fuzzy neural network model
can be build by using the methods introduced in Section 4.4.1. Since the input materials’
composition is steady in production process, there are no need to build different
decision-making models for different types converter slag as in a smelting furnace.
Fig. 4.6
Electric furnace for cleaning slag
In order to recover cobalt and nickel from converter slag, liquid converter slag
is smelted in a slag cleaning furnace. Sulphide is applied to sulphurize the
valuable metals and make them go into matte; quartzite is slag-making flux; coke
powder is reducer. The operation process is divided into melting stage and
cleaning stage: input materials in the melting stage; matte and slag are separated
in cleaning stage. This technological process is similar to a submerged arc
furnace mentioned in Section 4.3.
The main controllable variable of a slag cleaning process are input of converter
slag, quartzite, coke powder, power, output of cobalt enriched matte and cleaned
slag. In real production process, operation instructions are made in previous shift.
Limited by converter process and other conditions, the real input of converter in
this shift is often different from the amount given by instructions, while operators
often do not adjust other controllable variables such as the input of quartzite, coke
powder, the output of cobalt enriched matte and so on according to the difference,
therefore, it is difficult to make the smelting process running under an optimum
condition.
If the optimal input of sulphide, quartzite and coke powder were estimated
according to furnace state, output and composition of converter slag, then the
optimal load current and its duration time in the melting stage and cleaning stage
could be decided according to furnace state and input materials, finally, the