Mei C., Zhou J., Peng X. Simulation and Optimization of Furnaces and Kilns for Nonferrous Metallurgical Engineering

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

Thermal Engineering Processes

Simulation Based on Artificial

Intelligence

Xiaoqi Peng and Yanpo Song

Because of the complexity of nonferrous metallurgical processes, it is difficult to

build accurate mechanistic models for them. While, artificial intelligence(AI)

modeling method avoids the complex mechanism analysis and describes the object

process by its historic data, therefore, it is very advantageous especially for

complex industrial process in which historic process data have been accumulated

plentifully. In this chapter, several important AI methods and their applications are

introduced, based on these, two AI modeling methods for multi-variable systems

are proposed: one is fuzzy adaptive modeling method, which has been applied to

develop the fuzzy adaptive optimal decision model of the submerged arc furnace;

another is fuzzy neural network adaptive modeling method, which has been

applied to develop fuzzy neural network adaptive optimal decision model of the

electric furnace for cleaning slag. Both of the models are self-learning and

self-adaptive, and are able to avoid the disadvantage of the static decision-making

model based on the calculation of material balance and thermal balance in a

smelting process. They have achieved good performance in practice.

4.1



Characteristics of Thermal Engineering Processes in

Nonferrous Metallurgical Furnaces

There are many kinds of nonferrous metals, and their extraction processes are

  Xiaoqi Peng and Yanpo Song

very complex. Nonferrous metallurgical furnaces, as key equipments, are mostly

special furnaces without wide applications. Therefore, they have many

characteristics which are different from some general industrial furnaces such as

boiler, heating furnace, industrial furnace for steel making and so on:

a) There are too many operational variables, including chemical components and

physical characters of raw materials and fuel, technical conditions of furnace

operation and others. Furthermore, they are changing randomly in different extent.

b) There are serious coupling problems among multiple processes, such as heat

transmission, chemical reactions, phase change, and flow of fluid or melt, which

are often mutually conditional and interact fiercely.

c) There exists time delay in getting information of process detecting or

artificial monitoring.

d) Since the scale and yield of nonferrous metals production are relatively

small, basic research about it is not systemic enough, and some correlated thermal

physical parameters, especially, the dynamical parameters about a process are

deficient. Therefore, the mechanistic simulation models for these thermal

engineering processes are not only difficult to develop, but also difficult to

represent real processes. For example, to develop a mechanistic simulation model

for the process of copper-matte converting, just the static model needs nearly 20

equations even if the influence of dynamical factors has been ignored. While, this

analytical model could not be very precise because too many model parameters

are lost. Furthermore, too complex computation would influence the real-time

character of online control software.

When real production data are enough, it is proposed to model using AI

(artificial intelligence) methods, which can overcome the difficulties in modeling

arose from above-mentioned characteristics of nonferrous metallurgical furnace

in some satisfying extent.

4.2



Introduction to Artificial Intelligence Methods

Since control theory was created by American scientist, Norbert Wiener, in 1940s,

it has gained rapid progress and developed from the classic to the modern control

theory. However, the controlled objects and processes are often extremely

complex because of the problems such as complex nonlinearity, time-changing,

serious coupling, random disturbances, complex reaction mechanism, besides,

errors and delay exist in data measurement, the construction and dynamic

characteristics are uncertain, high control performance are required, so neither the

classic nor the modern control theory based on accurate mathematical model can

work with good performance. Therefore, AI system emerged as the requirements

of the times, which has good abilities of intelligent information processing,

4 Thermal Engineering Processes Simulation Based on Artificial Intelligence 

intelligent feedback and intelligent control.

AI means the abilities of some machines to execute some complex functions

concerned on human intelligence such as judgment and decision-making, image

identifying, learning and understanding etc. AI, which based on a symbol system

and information processing, is an important branch of computer science. The

main research fields include: natural language processing, logic deduction and

automated theorem proving, intelligent data retrieval system, robot and its visual

system, automated programming, expert system and so on.

In 1965, Chinese American scientist K.S. Fu first proposed applying heuristic

rules of AI theory to learning control systems (Fu, 1965). In 1971, after studying

the relationship between intelligence technology and learning control, he put

forward the concept of intelligent control (Fu, 1971), and pointed out that

intelligent control is the cross of control theory and AI technology (that is the

“binary elements theory” of intelligent control), which combines AI theory and

technology with control theory and technology. In unknown environment, human

intelligence is simulated so that system control can be realized effectively. In

1977, after proposing that intelligent control is the cross of control theory,

operation research and AI technology (that is the “three elements theory” of

intelligent control), G.N.Saridis proposed hierarchically intelligent control

(Saridis, 1977), namely, the structure of intelligent control can be divided into

three hierarchies from top to bottom: organization, coordination and control, the

precision of control increases in turn, while intelligence degree decreases in turn.

Since then, the research and application of intelligent control attracted more and

more attention from many countries. Especially, fuzzy logic control, neural network

control and expert control, as three typical intelligent control methods, have

absolute superiority to traditional control methods, and can control effectively

complex systems with the characteristics of nonlinear, multiple variables, long time

delay, strong coupling and so on, therefore, they have been widely applied in

engineering. At present, combining the abilities such as parallel learning,

remembering and associating of neural network with fuzzy reasoning technology to

form a self learning fuzzy controller (Zhang and Li, 1995), combining expert

system theory and technology with fuzzy logic technology to form an expert fuzzy

control and decision making system have been become the important trends in the

field of intelligent decision making and control (Wang, 1994).

4.2.1



Expert system

Intelligent control is essentially control based on knowledge. Special knowledge of

some fields can be divided into two classes: one is quantitative knowledge which

can be expressed by a precise mathematical model; another is empirical and

  Xiaoqi Peng and Yanpo Song

qualitative knowledge which can not be expressed by a precise mathematical model

but it can be expressed by heuristic rules in general. In dealing with difficult

problems of some fields, it is usually the latter knowledge that the experts’

judgment, forecasting and decision-making lies on, therefore, the empirical and

qualitative knowledge is the key of expert capability (Joseph and Gary, 2006).

Converting this kind of knowledge into a computer program, the program can

execute reasoning and decision making in the level of human experts, this program

is called expert system (Cai and Xu, 2004). Combining expert system theory and

technology with control theory and technology, simulating expert intelligence to

control system, this control is called expert control, and the system is called expert

control a system (Zhang and Sun, 1995). Its essence is that it can realize

optimization decision making and control by simulating human experts.

Expert system is a man-machine system with special knowledge to understand and

solve problems in some fields, such as explaining, forecasting, diagnosing, designing,

planning, monitoring, repairing, guiding, control and so on. Its performance lies on

completeness and accuracy of special knowledge, and the key to develop expert

system is knowledge expression and reasoning. The usual methods of knowledge

expression include: predicate logic, temporal logic, framework, process, semantic

network, Petri-Net, production rule, qualitative model, neural network production rule

and metasymthesis, in which the latter four methods have significant value for expert

control. While the usual reasoning methods include reasoning based on rules, fuzzy

logic reasoning, reasoning based on neural network, qualitative reasoning, reasoning

based on case and synthesis reasoning (Li, 2004), in which the former three methods

have been widely applied in expert control systems.

After the idea that introducing expert system technology into automatic control

was proposed in 1983, K.J. Astron

(Astron, 1986) proposed the concept of expert

control in 1986. With the aid of expert system technology, traditional control

engineering algorithms and heuristic logic reasoning were combined to develop

an expert control system, which integrate many logic control functions and can

adopt different control strategies according to different situations.

Comparing with the traditional control, expert control has the characteristics as follow:

a) It can collect knowledge and experience from many experts in some fields,

so its ability may be better than individual experts.

b) It can control effectively some complex industry processes which can not be

expressed in precise mathematic models.

c) It has self-learning ability and self-adaptive ability.

4.2.2



Fuzzy simulation

In 1965, when studied on modeling for the process of thinking and judgment, L.A.

4 Thermal Engineering Processes Simulation Based on Artificial Intelligence 

Zadeh (Zadeh, 1965, 1975) proposed using fuzzy set to quantify the process of

thinking and judgment. Therefore, the fuzzy set theory was created, which

provided a powerful tool for describing and processing fuzziness and

uncertainties of systems and simulating human functions such as fuzzy logic

thinking, judgment and decision-making. In 1973, L.A. Zadeh (Zadeh, 1973)

gave the definition and theorem of a fuzzy logic controller, which laid the

foundation for fuzzy control. In 1974, E.H. Mamdani (Mamdani, 1974) applied

successfully fuzzy logic in the pressure control and the speed control of a boiler

test equipment and a steam turbine engine for the first time, and opened the

research field of fuzzy logic controllers based on the fuzzy language control rules.

In 1979, he developed a self organizing fuzzy controller cooperating with T.J.

Procky (Procky, 1979). This controller could continuously modify control rules to

improve control performance in a control process, so it has good artificial

intelligence. Since then, fuzzy control has been successfully applied in complex

industrial processes, home appliance field, high-tech field and so on. Fuzzy

technology has shown such a great application potentiality that it was called core

technology in the 21st century (Li, 2004; Liu, 1997; Wang, 1987; Li, 1993).

In 1992, Kosko Bart proved that an addition fuzzy system, as a kind of structural

numeric estimator, could approach to any continuous function in compact domain

with any precision (Kosko, 1992a, b); Lixin Wang proved that fuzzy system with

production reasoning, central defuzzification and Gaussian- type membership

function can also approach any real continuous function in any closed subset with

any precision (Wang, 1992); Their research shows that fuzzy systems have strong

ability to express human knowledge, and provide a strong theoretical foundation for

building a fuzzy optimization decision-making and control system.

Fuzzy set theory can quantify human qualitative thinking, judgment and

decision-making. Therefore, when controlling or making decisions, besides the

information measureo directly can be used, the information obtained by human

sensory can be used also. Furthermore, these information are suitable for

computer processing. As the research results around the world, comparing with

the traditional control, fuzzy control based on fuzzy set theory, fuzzy language

variable and fuzzy logic reasoning has the characteristics as follows:

a) Because it uses language as expression method and does not need to build a precise

mathematic model for the controlled process, it can control effectively some complex

industry processes which could not be expressed by an exact mathematic model.

b) For industrial fieldwork operators possessing certain experiences, the control

and decision making methods described by the fuzzy rules are easier to master.

c) Man-machine communication can be realized by the nature language, so

process control can be realized effectively.

d) Dynamic response characteristic of a fuzzy control system is usually better

than conventional PID control, and has better robustness and self-adaptability.

  Xiaoqi Peng and Yanpo Song

4.2.3



Artificial neural network

Human intelligent activities such as thinking, association, memory, judgment,

decision-making and so on occur in brain, which is composed of huge amounts of

neurons. Different neurons connect one another in some modes and form a biological

neural network, and the connection strength between the neurons of the network can

change adaptively according to external actuating signals. Neuron shifts the states

between excitatory and inhibitory with the change in its received actuation signals.

The learning process of brain is the process in which the connection strength between

neurons change adaptively with external actuation signals. The results of information

processing in brain are expressed by the states of neurons. ANN (artificial neural

network) is an information processing system which simulates the structure and

function of the biological neural network by engineering technologies. It is composed

of a number of simple processing cells which simulate biological neurons and which

are connected on another in some way, and its ability to process information relies on

the cells’ dynamic response to the external input information.

In 1943, psychologist W. Mcculloch and mathematician W. Pitts proposed

cooperatively the earliest neuron model, which opens the era of neural science (Zhang,

1996; Hu, 1993). In 1949, D.O. Hebb (Hebb, 1949) proposed a hypothesis that

synapse connection strength is changeable, and learning process is thought as

occurring in synapses whose connection strength changes with the connecting neurons’

activities on its two ends. The learning rules based on this hypothesis laid a foundation

for the learning algorithm of artificial neural network. In 1958, F. Rosenblat proposed a

perceptron model to simulate human abilities of perception and learning for the first

time, and designed the perceptron which was capable of self learning and self

organizing. But in the book Perceptron published in 1969, the famous scientists M.

Minsky and S. Papert proved theoretically that the monolayer perceptron had only

limited ability. Furthermore, they speculated that the multilayer perception also had the

limitation, which throw a damp over the research on neural network (Zhou, 1993). In

early 1980s, after concentrating study, famous physicist J.J. Hopfield introduced the

concept of energy function, proposed HNN model, presented criteria for the stability of

neural network and pointed out that an electrical circuit composed by operation

amplifiers could be used to simulate neurons. His outstanding results revived the

research on ANN, and many researchers from the world were inspired to throw

themselves into this field. Therefore, ANN theory and application research got rapid

development, and new models and new theories constantly emerged (Hopfield, 1982,

1984). In 1983, G.E. Hinton and T.J. Sejnowski (Hinton and Sejnowski, 1986)

combined the output function of a neuron with Boltzmann distribution of statistics, and

proposed Boltzmann model. In 1987, B. Kosko (Kosko, 1987, 1988) proposed a

4 Thermal Engineering Processes Simulation Based on Artificial Intelligence 

bidirectional associative memories model. Also in 1987, Hecht Nielsen (Hecht, 1987)

proposed counter propagation neural network. Noticeably, a multi-layer back

propagation neural network proposed by P.J. Werbos (Werbos, 1974) in 1974 revived

and has been become one of the most widely applied networks at present. The research

on the neural network theory and application is heading for the climax, and it has been

widely applied in fields such as computer science, artificial intelligence, automatic

control, robot, information procession and so on.

ANN, as a simulation of human brain, is a kind of nonlinear dynamic system in

essence. Comparing with other information process systems, its characteristics

are as follows (Deng, 1994):

a) It expresses special information by the connections among lots of neurons

and their weights, that is, its information storage way is distributed, so it has

strong robustness and fault tolerance, and can recover efficiently information

even if some local neurons are damaged.

b) It has the abilities of parallel and cooperation information processing and

reasoning.

c) It has the abilities of self-learning, associative memory and synthesis reasoning,

and can process various signals and patterns which simulate human brain.

d) It can approach any nonlinear function with any precision.

Because of the advantages mentioned above, it has great potential in

controlling the complex system with high nonlinearity and high uncertainty.

Therefore, it has been widely applied in the field of process decision-making and

control. Generally, the control based on ANN is called NNC (neural network

control) or NC (neural control). The roles of ANN in NC are as follows:

a) Serving as an object model in the structure of control based on a precise model.

b) Serving as the controller in a feedback control.

c) Serving for the functions of optimizing decision and computing in a control system.

d) Combining with other intelligent control methods and optimization algorithms,

and providing them with nonparametric models, reasoning models, optimized

parameters and so on.

4.3



Modeling Based on Intelligent Fuzzy Analysis

Most industrial processes are generally complex systems with characteristics such as

multi-variable, non-linear and long time-delay. Therefore it is very difficult to make

optimal decision by mathematical analysis, though the experienced spot workers can

do it according to their abundant experience. This experience knowledge contained in

huge amount of real production data and accumulated in operation is generally

described as fuzzy rules, and it is very possible to extracted this usefue knowledge by

fuzzy model. In this section, practical algorithms of fuzzy model identification and

adaptive optimization for multi-variable system are proposed and applied to a typical

  Xiaoqi Peng and Yanpo Song

complex industrial systemüa nickel-matte smelting submerged arc furnace. A fuzzy

adaptive optimal decision-making model was developed as well to achieve the goals

of energy-saving and consumption-reduction.

4.3.1



Intelligent fuzzy self-adaptive modeling of multi-variable system

Providing a system with r inputs )(tx

(i=1,2,…,r) and q outputs )(ty

(j=1, 2, …,

q), the value of any input

)(kx

at time k is decided by L fuzzy rules, these L

rules constitute the fuzzy decision model of this input, in which the lth rule R

can

be expressed as follows (Tomohiro and Michio, 1985):

)1(

−kx is

A , )2(

−kx is

A ,…, )(

nkx − is

)1( −kx

A , )2( −kx

A ,…, )( nkx

− is

A ,

)1(

−ky is

B , )2(

−ky is

B ,…, )(

nky − is

)1( −ky

B , )2( −ky

,…, )( nky

− is

B ,

then

0111 121 11

() ( 1) ( 2) ( )

lll l l

xk a axk axk axk nK=+ −+ −++ −+

21 2 22 2 2 2

(1) (2) ( )

ll l

axk ax k axk nK−+ − + + − +

(1) (2) ( )

ll l

rr r r rnr

ax k ax k ax k nKK+−+ −++−+

11 1 12 1 1 1

(1) (2) ( )

ll l

byk byk b yk mKK−+ − + + − + +

(1) (2) ( ) ()

ll l l

qq q q qmq

km ekK−+ − + + − +

(4.1)

where

)(kx

and )(ky

are the values of

x and

y at k time; )(ke

is the

error of fuzzy rule;

and

denote the fuzzy subsets of

x and

in the domains of input and output respectively, defining these fuzzy subsets

needs to consider the special condition of an object, in this paper they are defined

as shown in Fig.4.1, triangle subordination degree functions are chosen;

a and

b are model parameters that need to be identified; )(kx

is the input control

variable decided by the lth fuzzy rule; n, m are the orders of a model.

Fig. 4.1 Fuzzy sub-sets A

and B

4 Thermal Engineering Processes Simulation Based on Artificial Intelligence 

Given a group of data [

)1(

−kx

)2(

−kx

,( )xk n−K,,(1)

xk−K,(2),

xk− K,

)( nkx

− ,

,( 1)yk−K,)2(

−ky ,

,( )yk m−K,,(1)

yk−K,(2),

yk− K,

)( mky

− ], input control variable )(kx

can be got by weighted averaging

)(kx

decided by L decision rules:

() ()

ili l

xk xk

λλ

∑∑

• (4.2)

where weight

can be got as follows:

11 11

[( )] [( )]

rn m

lj lj

lAi Bi

ij ij

xk j yk j

λμ μ

== ==

=− −

II III

(4.3)

where “

Ι ” expresses “and” in fuzzy logic, namely minimizing operation;

)]([ jkx

−

expresses the membership function value of

)( jkx

−

for fuzzy

subset

A , the mean of )([ jky

−

is similar.

4.3.1.1



Identification of fuzzy decision making model of multi-variable

system

(Peng et al., 1994)

By combining the mechanism analysis and the multiple linear stepwise regression

method (Wu, 1987), n and m can be decided. If they are small, model parameters

can be got by the following identification algorithm, otherwise, the input or

output variables with weaker effect should be ignored in order to speed up the

identification algorithm. Let

0 11 12 1 1 2 11 12 1 1 2

[]

ll l l l l l l l l l l l T

lnrrrnmqqqm

aa a a a a a bb b b b bKK K KK K=θ

(4.4)

11 1

[1 ( 1) ( 2)] ( ) ( 1) ( 2)

()(1)(1)(2)( )

(1)(2) ( )

qq q

xk xk xk n xk xk

xk nxk yk yk yk m

yk yk yk m

KK K

=−− − − −

− −−− −

−− −

then, Eq. 4.1 can be rewritten as:

() ()

lTl

xk ek=+θ

(4.6)

Substitute Eq. 4.6 into Eq. 4.2, then

11 1

() ()

TT Tl

i Ll

LL L

ll l

xk ek

λλ

λλ λ

== =

=++++

∑

∑∑ ∑

Kθθ θ

ϕ ϕ ϕ

(4.7)

Let

∑

ϕ ϕ

(4.8)

[]

lTTTT

= K

ϕ ϕ ϕ ϕ

(4.9)

[]

= KΘ

θ θ θ

(4.10)

() ()

ek ek

∑

(4.11)

(4.5) (4.5)

  Xiaoqi Peng and Yanpo Song

then Eq. 4.7 can be rewritten as:

() ( ) ()

iii

xk ek=+Θ

(4.12)

This expression is called the control model of input variable

)(kx

, in which

is parameter vector,

is innovation vector and, it is a constant vector

converted from the first set of data according to Eq. 4.3, Eq. 4.8 and Eq. 4.9.

According to a control objective, the quality of real production data can be judged

by some performance indexes, while the data groups whose performance indexes

meet the requirements are called optimal data groups. In order to get the optimal

rules, optimal data groups should be used to identify the model parameters.

Therefore, selecting N different optimal data groups from real production data

(where N should not be less than the number of parameters), according to Eq. 4.3,

Eq. 4.5, Eq. 4.8 and Eq. 4.9, innovation vectors

,…,

can be found.

Substituting N optimal data groups and their innovation vectors into Eq. (4.12),

we have:

[ ( ) ( ) ( )] [( )( ) ( )] ()

TTTNTT

ii iN i

xkxk xk kKK=+Θ e

ϕ ϕ ϕ

(4.13)

where,

() [()( ) ( )]

ii iN

kekekekK=e (4.14)

Let

[()() ( )]

iii iN

xkxk xkK=x (4.15)

[( ) ( ) ( ) ]

TT NTT

ϕ ϕ ϕ

(4.16)

then, Eq. 4.13 can be converted to:

()

k=+x Θ e

(4.17)

By means of the least square parameter estimation method(Wu,1987), the best

estimation for parameter vector

of fuzzy control model of )(kx

is:

[]

−

φ φ φ

(4.18)

4.3.1.2



Fuzzy adaptive optimization algorithm

The performance of a decision-making may be gradually declining due to the

slowly-varying of external environments, production conditions and system

structure. To make a model have the capability of self-learning and self-

adaptation, obsolete rules in original model should be replaced dynamically by

new fuzzy decision rules based on new optimal data groups, and then new

can be obtained. To reduce the computational complexity and speed up the

identification, recursive least square method with moving range(Wu,1987) are

usually used to revised the model adaptively.

Identification algorithm of fuzzy a adaptive control model can be shown as

Fig.4.2.