J. Cent. South Univ. (2017) 24: 2222−2230 DOI: https://doi.org/10.1007/s11771-017-3631-5

Flatness predictive model based on T-S cloud reasoning network implemented by DSP

ZHANG Xiu-ling(张秀玲)1, 2, GAO Wu-yang(高武杨)1, LAI Yong-jin(来永进)1, CHENG Yan-tao(程艳涛)1

1. Key Laboratory of Industrial Computer Control Engineering of Hebei Province,

Yanshan University, Qinhuangdao 066004, China; 2. National Engineering Research Center for Equipment and Technology of Cold Strip Rolling,

Yanshan University, Qinhuangdao 066004, China

© Central South University Press and Springer-Verlag GmbH Germany 2017

Abstract: The accuracy of present flatness predictive method is limited and it just belongs to software simulation. In order to improve it, a novel flatness predictive model via T-S cloud reasoning network implemented by digital signal processor (DSP) is proposed. First, the combination of genetic algorithm (GA) and simulated annealing algorithm (SAA) is put forward, called GA-SA algorithm, which can make full use of the global search ability of GA and local search ability of SA. Later, based on T-S cloud reasoning neural network, flatness predictive model is designed in DSP. And it is applied to 900HC reversible cold rolling mill. Experimental results demonstrate that the flatness predictive model via T-S cloud reasoning network can run on the hardware DSP TMS320F2812 with high accuracy and robustness by using GA-SA algorithm to optimize the model parameter. Key words: T-S cloud reasoning neural network; cloud model; flatness predictive model; hardware implementation; digital signal processor; genetic algorithm and simulated annealing algorithm (GA-SA)

1 Introduction

Strip steel is the primary product of rolled steel, and it is diffusely utilized in bridges, cars, buildings and ships. Flatness is one of key quality indexes of strip product. Flatness predictive is the important technique in strip mills for flatness control [1, 2]. However, there are many external or internal causes, which makes it difficult to get an accurate mathematical model for flatness predictive. The rolling process is non-linear, time varying, strong coupling and multivariate. So, an in-depth and all-round study on flatness predictive theory is necessary for the development of flatness predictive technique [3].

With the great development of artificial intelligence science, many effective models and algorithms are applied to flatness predictive and flatness control. The single nerve-cell adaptive PID flatness control based on back propagation (BP) neural network was proposed [4]. The method can improve the predictive accuracy and obtain good anti-interference ability. For improving the predictive accuracy of conventional flatness predictive method, the flatness intelligent predictive model based

on GA-PID neural network (GA-PIDNN) was proposed [5]. This approach can increase flatness predictive accuracy and speed effectively. A novel flatness predictive approach based on extreme learning machine (ELM) was proposed [6]. This method can not only enhance the predictive accuracy, but also has strong generalization ability. But in aforementioned references, flatness predictive precision is limited and experiment belongs to software simulation. What is more, these methods can not be directly used to practical engineering.

Based on fuzzy mathematics and probability theory, a novel model, named cloud model, was presented by LI et al [7]. The cloud model can not only reflect the ambiguity of natural language concepts, but also describe the correlation between ambiguity and randomness. Combining with T-S fuzzy neural network, the Gaussian membership function is replaced by cloud model, and then T-S cloud reasoning network is constituted. The introduction of the cloud model is to strengthen the ability of neural network deal with uncertain information. The GA-SA algorithm is proposed, which can make full use of the global search ability of GA and local search

Foundation item: Project(E2015203354) supported by Natural Science Foundation of Steel United Research Fund of Hebei Province, China;

Project(ZD2016100) supported by the Science and the Technology Research Key Project of High School of Hebei Province, China; Project(LJRC013) supported by the University Innovation Team of Hebei Province Leading Talent Cultivation, China; Project(16LGY015) supported by the Basic Research Special Breeding of Yanshan University, China

Received date: 2016−03−30; Accepted date: 2016−11−07 Corresponding author: ZHANG Xiu-ling, Professor, PhD; Tel: +86–18903339410; E-mail: zxlysu@ysu.edu.cn

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ability of SA. T-S cloud reasoning network optimized by GA-SA algorithm is put forward. Based on T-S cloud reasoning neural network, flatness predictive model is designed in DSP, and it is applied to 900HC reversible cold rolling mill. Experimental results confirm that GA-SA algorithm has such advantages: high optimization precision, less number of iteration and fast speed of convergence. Flatness predictive model based on T-S cloud reasoning network has high accuracy and robustness. The experimental results also verify that the flatness predictive model via T-S cloud reasoning network can run on the hardware TMS320F2812, so it provides basis for neural network applied to practical engineering. 2 Design of flatness predictive model via T-S

cloud reasoning network 2.1 Structure and principle of T-S cloud reasoning

neural network Definition 1: Suppose that U is a quantificational

domain expressed by exact value and C is a qualitative notion in U. If Ux and x is a stochastic realization on C, and the certainty degree ]1,0[)( x from x to C is a stochastic number with steady inclination:

]1,0[: U ,Ux x→μ(x) Then the distribution of x on field U is called cloud

and each x is called cloud particle [8]. Definition 2: Suppose that U is a quantificational

domain expressed by exact value, Ux and x is a stochastic realization on C, 2~ ( , ' )x N Ex En and

2' ~ ( , ),En N En He the certainty degree μ from x to C is 2

2

( )exp

2( ')

x Ex

En

(1)

Then the distribution of x on field U is called

normal cloud [8]. The three digital features: expected value (Ex),

entropy (En) and hyper entropy (He) are utilized to represent the notion of clouds. Normal cloud and three digital features are shown in Fig. 1.

Ex is the distributive expectancy of cloud particle in the space of field and the most typical point of the qualitative notion. En is a survey of the indetermination of the qualitative notion, and it is determined by the notion of ambiguity and randomness. On the one hand, it is a survey of ambiguity of the qualitative notion and reflects the scope of cloud particles in the space of field. On the other hand, it is a survey of randomness of the qualitative notion and mirrors the dispersion degree of cloud particles. He is a survey of the indetermination of En.

Based on the above, T-S cloud reasoning network is designed. The structure of T-S cloud reasoning network

is shown in Fig. 2. It has two sections: the premise section and the latter section. The premise section is utilized for matching the cloud vague regulation’s premise, and the latter section is utilized for generating the cloud vague regulation’s latter.

Fig. 1 Normal cloud and three digital features

Fig. 2 Structure of T-S cloud reasoning network

The premise network includes three layers: The first layer is called input layer, and input

variables are transported into premise section by it. It contains n codes.

The second layer is called cloud layer. Each node stands for a cloud model. In this layer, each input value is clouded into m sections. The amount of node is n×m.

The third layer is called cloud reasoning layer. Each node stands for a cloud regulation. The output of premise section is a fitness degree of a cloud vague rule. It is usually expressed in the form of algebraic product:

1 21

, 1, 2, , n

j j j nj iji

k k k k j m

(2)

There are m nodes in this layer.

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The latter section includes three layers: The first layer is called input layer, and input

variables are transmitted to the second layer. x0=1 is utilized to furnish the constant terms for the cloud vague regulation’s latter in this layer.

The second layer contains m nodes. Each node stands for a regulation and it is utilized to compute the latter of each regulation. The outputs are:

00

( 1)n

k kj i ji

i

yi x w x

(3)

where 1, 2, , ; 1, 2, , .k r j m r is the dimension of the network’s output.

The third layer is utilized to compute the overall output of the network:

1

1

mk

j jj

k m

jj

yi

y

(4)

When there are p samples of inputs network, the

total error is the square sum of the each output error for each sample:

21

1

2

r

p k kk

E d y

(5)

where dk is expected output.

After whole studying sample inputs network, the total error E is obtained:

21 1 1

1

2

q q r

p k kt t k

E E d y

(6)

where q is the amount of samples. 2.2 Design of flatness predictive model for rolling mill

A six-high 900HC reversible cold rolling mill is taken as research object in this work. Flatness defect identification is the foundation of flatness predictive [9]. Taking the diversity of modern mill flatness predictive means and demand of predictive accuracy into consideration, right-one-third waves and left-one-third waves were added on the basic of the conventional six fundamental flatness patterns [10–12], which makes the flatness fundamental patterns more self-contained. Therefore, at present the fundamental pattern of flatness mainly contains right waves, left waves, double-edge waves, center waves, left-one-third waves, right-one- third waves, edge-center waves and quarter waves.

The rolled flatness can be expressed as the linear combination of the fundamental pattern [13]:

1 1 3 2 5 3 7 4( )f y u p y u p y u p y u p y (7)

where 21 2

3 1, ,

2 2p y y p y y 3

31

( ) (5 3 ),2

p y y y

4 24

135 30 3

8p y y y and 1 2, ,p x p x

3p x and 4p x stand for linear, quadratic, cubic, and

quartic Legendre multinomial respectively. 1 ,p x

2 ,p x 3p x and 4p x stand for left waves,

right waves, center waves, double-edge waves, right- one-third waves, left-one-third waves, quarter waves and edge-center waves, respectively. u1, u3, u5 and u7 stand for flatness defects membership. Their sizes stand for the content of corresponding flatness defect and the symbols of them reflect the types of flatness.

For improving the predictive accuracy of flatness, much more factors which affect flatness should be considered. The number of inputs is 17. They are the fundamental rolling parameters: entrance average thickness of strip h0, exit average thickness of strip h1, initial width of strip B, back tension T0, front tension T1, rolling force F, work roll diameter Dw, backup roll diameter Db, rolling temperature T, intermediate roll diameter Dm, and elastic modulus of elasticity E. The rolling adjustment parameters are force of work-roll bending Fw and intermediate roll-shift δ. The flatness memberships of the k time are u1(k), u3(k), u5(k) and u7(k). The outputs of prediction model are the flatness memberships of k+1 time: u1(k+1), u3(k+1), u5(k+1) and u7(k+1). Then a 17-input 4-output flatness predictive model is designed based on T-S cloud reasoning neural network. The inputs and outputs of the network are as follows: Inputs: 0 1 1 0[ , , , , , , , , , ,w m bU B h h F T T D D D T

T1 3 5 7, , , ( ), ( ), ( ), ( )]wE F u k u k u k u k

Outputs: T7531 )]1( ),1( ),1( ),1([ kukukukuY

The structure of flatness prediction model is

displayed in Fig. 3.

3 Combination of GA and SA algorithms

Genetic algorithm has strong global search ability, but also has poor local search ability. Simulated annealing algorithm has strong local search ability, and enables the search process to avoid falling into local optimal. But it does not know much about the whole search space and it is not easy to make the search process into the most promising search area. Therefore, the operation efficiency of simulated annealing algorithm is not high. If we combine genetic algorithm and simulated annealing algorithm together, we may develop a new global search algorithm with excellent performance.

From the above discussion, a new hybrid algorithm genetic simulated annealing algorithm (GA-SA) is proposed in this work. In GA-SA algorithm, in order to make full use of the strong global search ability of GA, GA is firstly used to optimize fitness function. When meeting the termination conditions of GA, it will output

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Fig. 3 Structure of rolling mill flatness predictive model

the optimal individual. Then to take advantage of the strong local search ability of SA algorithm, SA algorithm is continuously used to optimize the fitness function through letting the optimal individual obtained by GA as the initial individual of SA algorithm. When meeting the termination conditions of SA algorithm, it will output the optimal individual of GA-SA algorithm.

In order to make GA-SA algorithm simple, effective, fast, GA toolbox and SA algorithm toolbox are adopted to optimize the fitness function. In GA toolbox, only population size, termination generation, crossover probability and mutation probability need to be set [14]. The parameters of SA algorithm toolbox mainly include: initial individual value and termination generation to be set. The introduction of algorithm toolbox makes GA-SA algorithm more rapid, beneficial and effective for engineer from the aspects of programming, optimization process, and optimization precision. At the same time, algorithm toolbox provides a great possibility for GA-SA algorithm applied to practical engineering. The flow chart of GA-SA algorithm is shown in Fig. 4.

GA-SA algorithm is utilized to optimize the parameter of predictive model. According to the structure of T-S cloud reasoning network, there are 212 variables needed to be optimized. In GA algorithm, population size is 20, stopping generations are 2500, crossover probability is 0.8, and mutation probability is 0.2. In SA algorithm, termination generations are 2500. Equation (6) is selected as the fitness function. The optimization objective is to get the minimum of fitness function value. The optimize process of GA-SA algorithm is shown in Fig. 5.

Fig. 4 Flow chart of GA-SA algorithm

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Fig. 5 Optimize process of GA-SA algorithm

4 Flatness predictive model designed and implemented by DSP

4.1 Background of neural network implemented by

DSP Artificial neural network has strong ability of

nonlinear fitting, memory and self-learning. It can map any complex nonlinear relation [15]. The learning rule of neural network is simple and easy to implement by computer. Therefore, neural network is widely used in pattern recognition, image recognition, intelligent robot, predict estimate, system identification, and other fields [16–18]. But the neural network algorithm has less successfully applied to practical engineering. The reasons for this are as follows:

1) The calculation of neural network is big. It is difficult to meet the real-time requirement of engineering via the processor of Von Neumann structure to achieve the function of neural network by software programming approach [19]. The method of software programming is just software simulation, and neural network cannot be directly applied to practical engineering;

2) Even if chip manufacturers are trying to develop all kinds of special chip for neural networks, the price of chip is high, and the development is still at an early stage. So, it still needs a period of time to the actual application of special chip.

With the vigorous development of microelectronics technology, the microprocessor which is not von Neumann structure appears. TI’s digital signal processor (DSP) is one of the representative products. DSP gives up the traditional structure of von Neumann, and adopts the advanced structure of Harvard bus [20]. What is more, DSP has rapid accumulation instructions in single cycle, dedicated hardware multiplier, and quick instruction cycle. So, the data throughput is one time higher. The appearance of DSP realizes some occasions which are restricted by the speed and structure of traditional microprocessor. Thus DSP can meet the speed

requirement of complex algorithm. What is more, DSP can connect to the peripheral device, so as to realize the control for the peripheral equipment. 4.2 Flatness predictive model implemented by DSP

The implementation of neural network is an important factor for whether theoretical results are applied to practice effectively. There are many ways about how to apply the simulation results of network to practical engineering. Usually, the realization of the neural network is divided into hardware and software implementation. The realization of neural network algorithm by software method is limited by the computer frequency. And software cannot connect to complex peripheral, therefore software implementation of neural network algorithm cannot be directly used to practical engineering. But the realization of neural network algorithm by hardware method can accelerate the operation speed of neural network, and hardware can realize the control for peripheral equipment through connecting to complex peripheral. Therefore, hardware implementation of neural network can be applied to engineering.

In this work, TMS320F2812 of Texas Instruments is chosen to perform the DSP implementation of the flatness predictive model. It not only has powerful ability of digital signal processing, but also has relatively perfect ability of time management and embedded control. It is widely used in industrial control, especially in the field which needs high processing speed and high precision [21].

In the DSP implementation of the flatness predictive model, firstly, the program of flatness predictive model via T-S cloud reasoning network in DSP is written based on the program of flatness predictive model via T-S cloud reasoning network in MATLAB. Then the parameters of T-S cloud reasoning network are optimized by GA-SA algorithm in MATLAB and these parameters are transmitted to DSP later. The flatness predictive model runs in MATLAB and DSP separately. Finally, the two results of flatness predictive model, which runs in MATLAB and DSP respectively, are compared and analyzed. The flow chart of flatness predictive model designed and implemented by DSP is shown in Fig. 6.

The essence of flatness predictive model designed and implemented by DSP is to send input signal to the network in DSP and perform reasoning algorithms, the main use of which is the perfect multiplication and addition operation of DSP. 5 Simulation results and discussion

For testing the availability of the method presented

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Fig. 6 Flow chart of flatness predictive model designed and

implemented by DSP

above, flatness predictive model is applied to 900HC reversible cold-rolling mill. The rolling size specification of steel strip is: 2.2 mm×662 mm→0.247 mm×662 mm and the material of steel strip is steel plate hot commercial (SPHC). The rolling fundamental parameters are shown in Table 1. The test samples are all surveyed successive data from a rolling mill.

The flatness predictive model is set up by T-S cloud reasoning neural network. The training samples

Table 1 Basic rolling parameters

Basic input parameter Value range

Initial width of strip, B/mm 460–480

Entrance average thickness, h0/mm 0.24–4.00

Exit average thickness, h1/mm 0.24–1.50

Rolling force, F/kN 0–8000

Front tension, T1/kN 4–80

Back tension, T0/kN 4–80

Work roll diameter, Dw/mm 245–270

Intermediate roll diameter, Dm/mm 320–340

Backup roll diameter, Db/mm 790–850

Rolling temperature, T/°C 55–56

Young’s modulus of elasticity, E/MPa 21000

Work roll bending force, Fw/T 25.969–40.800

Intermediate roll shifting position, δ/mm –200–200

are normalized. There are flatness survey instrument at the channel of the first, third, and fifth passes in 900HC reversible cold-rolling mill. In order to test the validity of GA-SA, the flatness predictive model is optimized by GA-SA and GA respectively. Finally, the predictive results are compared with the surveyed flatness in the first, third, and fifth passes. The results are shown in Table 2. For more vivid and distinct, three dimensional pictures of flatness are shown in Figs. 7–9.

From Table 2 and Figs. 7–9, it is clear that the SSEs of GA-SA algorithm in the first, third and fifth passes are smaller than GA respectively. Predictive flatness of

Table 2 Results of predictive flatness and actual flatness

Pass No. Actual output GA-SA GA

Predictive output SSE Predictive output SSE

First

u1=0.6415 u1=0.6644

0.0014

u1=0.6654

0.0034 u3=–0.1489 u3=–0.1775 u3=–0.1502

u5=–0.6084 u5=–0.5953 u5=–0.6390

u7=–0.3012 u7=–0.3024 u7=–0.3413

Third

u1=0.8700 u1=0.8679

0.0002

u1=0.8331

0.0052 u3=–0.2120 u3=–0.2225 u3=–0.2058

u5=–0.7809 u5=–0.7882 u5=–0.7196

u7=–0.1604 u7=–0.1687 u7=–0.1558

Fifth

u1=0.6503 u1=0.6331

0.0011

u1=0.6003

0.0307 u3=–0.1155 u3=–0.0973 u3=–0.0381

u5=–0.4736 u5=–0.4533 u5=–0.4437

u7=–0.2638 u7=–0.2713 u7=–0.4096

Note: SSE represents the sum of squared errors between the actual outputs and the predictive outputs.

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GA-SA has better uniformity compared with the actual flatness. It can be known that flatness predictive model optimized by GA-SA is relatively superior. It furnishes a basis for flatness intelligent control.

In order to test the availability of flatness predictive model implemented by DSP, the prediction effects of the flatness predictive model in MATLAB and DSP are compared respectively. The results are shown in Table 3. The curve of the prediction results in MATLAB and DSP are shown in Fig. 10.

Table 3 and Fig. 10 show that the predictive results of the network under the environment of MATLAB and DSP are almost the same. It demonstrates that the flatness predictive model via T-S cloud reasoning network implemented by DSP has high robustness and accuracy. The run time of flatness predictive model in DSP is shorter than in MATLAB. It can meet the real-time request of flatness predictive. At the same time, the experimental results verify that the feasibility of flatness predictive model is implemented by DSP.

Fig. 7 Flatness three-dimensional diagrams at same moment in first pass: (a) Two-dimensional diagram of predictive flatness and actual flatness; (b) Three-dimensional diagram of predictive flatness; (c) Three-dimensional diagram of actual flatness

Fig. 8 Flatness-three dimensional diagrams at the same moment in the third pass: (a) Two-dimensional diagram of predictive flatness and actual flatness; (b) Three-dimensional diagram of predictive flatness; (c) Three-dimensional diagram of actual flatness

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Table 3 Results of predictive flatness in MATLAB and DSP

Pass No. MATLAB SSE DSP SSE Run time in MATLAB/s Run time in DSP/s

First 1.4×10–3 1.4×10–3 1.349×10–2 1.325×10–3

Third 2.0×10–4 2.0×10–4 9.831×10–3 1.324×10–3

Fifth 1.1×10–3 1.2×10–3 1.462×10–2 1.326×10–3

Fig. 9 Flatness three dimensional diagrams at the same moment in the fifth pass: (a) Two-dimensional diagram of predictive flatness and actual flatness; (b) Three-dimensional diagram of predictive flatness; (c) Three-dimensional diagram of actual flatness

Fig. 10 Flatness predictive curve: (a) Flatness predictive curve of the first pass; (b) Flatness predictive curve of the third pass; (c) Flatness predictive curve of the fifth pass

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6 Conclusions

1) The experimental results verify that the flatness predictive model via T-S cloud reasoning network can run on the hardware TMS320F2812 effectively demonstrating that the T-S cloud reasoning network based on DSP has a broad prospect in flatness predictive and other fields.

2) GA-SA algorithm has such advantages: high optimization precision, less number of iteration, fast speed of convergence and easy to utilize by engineer because of the use of GA toolbox and SA algorithm toolbox. It can make the flatness predictive model via T-S cloud reasoning network implemented by DSP with high accuracy and robustness.

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(Edited by FANG Jing-hua)

Cite this article as: ZHANG Xiu-ling, GAO Wu-yang, LAI Yong-jin, CHENG Yan-tao. Flatness predictive model based on T-S cloud reasoning network implemented by DSP [J]. Journal of Central South University, 2017, 24(10): 2222–2230. DOI: https://doi.org/10.1007/s11771-017-3631-5.