This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2015.2442223, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
1
Online Monitoring System Design for Roll Eccentricity in Rolling Mills Xu Yang, Member, IEEE, Hao Luo, Minjia Krueger, Steven X. Ding, and Kaixiang Peng
Abstract — This paper deals with the parameter estimation and online monitoring of roll eccentricity in rolling mills. The roll eccentricity-induced disturbances can result in strip thickness deviation and product quality degradation, and the conventional control strategy cannot regulate this kind of periodic disturbances due to its complex characteristics. For the purpose of product quality assessment and monitoring, a performance indicator based on product expectations or the empirical value of the quality related process variables, which can be visualized quantitatively with four zones, is proposed in the high level. In the low level, the key parameters of roll eccentricity are estimated in real-time using an adaptive observer for frequency estimation and an adaptive algorithm for amplitude and phase estimation. The performance and effectiveness of the proposed eccentricity monitoring system is demonstrated through a case study of cold rolling mill from industrial fields. Index Terms — Rolling mills, roll eccentricity, strip quality monitoring, performance indicator, adaptive system. I. I NTRODUCTION
T
HE hot/cold rolling process is a high speed, transient, and time-related metal machining molding process. The strip, which passes through roll gap and is extruded into different specifications of thin sheet, is the final output of steel production. In the strip production, the strip quality is one of the most important factors for consumer decision in the selection among competing products. The quality of the strip is expressed in terms of e.g. the thickness of the strip, the flatness of the strip and so on. There are many factors which can affect the strip thickness, leading thickness deviation or defects of rolled strips, and roll eccentricity problem is the most critical one among them [1]. In the past three decades, Manuscript received January 28, 2015; revised April 16, 2015; accepted May 13, 2015. Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to
[email protected]. This work was support by National Natural Science Foundation of China (51205018, 61473033), Fundamental Research Funds for the Central Universities (FRF-TP-14-121A2), Research Project of State Key Laboratory of Mechanical System and Vibration (MSV201409), Beijing Natural Science Foundation (4142035). (Corresponding author: Hao Luo.) Xu Yang and Kaixiang Peng are with the School of Automation and Electrical Engineering, University of Science and Technology Beijing, 100083, Beijing, China (emails:
[email protected];
[email protected]). Hao Luo, Minjia Krueger and Steven X. Ding are with the Institute for Automatic Control and Complex Systems (AKS), University of Duisburg-Essen, 47057, Duisburg, Germany (emails:
[email protected];
[email protected];
[email protected]).
the roll eccentricity issue has drawn much attention with the increasingly demands on higher quality, high ratio of yield and lower cost in modern strip rolling production. As a matter of fact, roll eccentricity commonly exists in a strip rolling process, generally caused by inexact rolls grinding, non-uniform thermal expansion of rolls, ovality of working rolls or backup rolls, etc. [2]. For the roll eccentricity compensation, it is fundamental to monitor and estimate the three key parameters(amplitude, frequency and phase) of periodic roll eccentricity-induced disturbance. Although the initial parameters of roll eccentricity can be measured and extracted via rolling force sensor from pre-loading experiment, which is executed without strip in steady rolling state. The situation cannot be exactly the same in actual dynamic rolling process. Consequently, it is extremely important to acquire key parameters of roll eccentricity online precisely and establish roll eccentricity control model for the following active regulation parts. Recently, great research efforts on process monitoring and fault diagnosis in rolling processes [3]–[5] and other industrial fields [6]–[10], have been made both from the model-based point of view [11], [12] and from the data-driven point of view [13]–[19]. As for the roll eccentricity monitoring and identification, the existing approaches can be classified into two groups: 1) Signal processing-based schemes: Fast Fourier transform (FFT) is a relatively simple and effective method by separating desirable and noise components from measurement signals, and is already made application in industrial fields. Because of its local contradiction between time and frequency domain, the sampling duration must be the integral multiple of eccentricity components period, while such condition cannot be satisfied in rolling process since the frequency of roll eccentricity always vary with the dynamic rolling speed. Although the modified FFT (MFFT) releases the above restriction by using difference evolution algorithm [20], it will lead to the decrease in computational efficiency. In contrast to FFT approach, the wavelet transforms analysis method [21] has good localization characteristics in both time and frequency domains, it is also unrestricted to sampling duration requirement and the influence by signal acquisition noise. But it should be noted that the frequency aliasing and redundant images [22] will emerge during wavelet decomposition and reconstruction process, therefore cannot guarantee the roll eccentricity components reflects the real situation in rolling mills. 2) Artificial intelligence-based schemes: Neural network and fuzzy logic have been introduced into roll eccentricity identification. Neural network technique is presented as a solution [23] for identifying the three key factors of roll
0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2015.2442223, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
eccentricity based on the measured angular velocity of rolls, but it can only identify fundamental wave, resulting in the limited compensation accuracy. Besides, there are big amounts of rolling mill stands without angular velocity sensors due to cost and economic considerations. The fuzzy-based methods as well as least-squares algorithm have also been developed for estimation of roll eccentricity, to distinguish the fundamental frequency wave and high eccentricity harmonic, but it can only be calculated and obtained offline [24] due to its complexity. Meanwhile, the monitoring and identification task is getting more complicated since the following aspects have to be taken into consideration: 1) Frequency, amplitude, and phase of roll eccentricity are not constant in dynamic rolling process. For instance, the threading situation as well as speed up/down situation, the rolling speed varies quickly, so as to the change of eccentricity frequency; the eccentricity amplitude will also change by the abrasion or thermal expansion of rolls; and even the eccentricity phase will not maintain constant as a result of stick-slip effect between working rolls and backup rolls. 2) The monitoring algorithm should run fast in order to avoid introducing delay into the following compensation system. And the final goal of monitoring and identification is to suppress periodic disturbance by roll eccentricity and avoid strip thickness deviation. Thus, in addition to consider the realtime requirement of algorithm itself, it is also necessary to design it to be operated together with the conventional control loop for AGC system. Strongly motivated by the aforementioned studies, the objective of this paper is to develop efficient online monitoring algorithm for the estimation of key parameters of roll eccentricity, which could be further integrated into the controller for the compensation of the effect due to roll eccentricity. In order to achieve that, we firstly give a general definition of quality assessment system to visualize the performance of the process. Furthermore, an adaptive observer is proposed for the online frequency estimation, as well as the adaptive algorithm for amplitude and phase estimation. The rest of the paper is organized as follows. In Section II, the structure of four-high (4-h) rolling mill, so as the strip gauge control system, is presented. Section III is devoted to a brief sketch of quality monitoring system. In Section IV, the roll eccentricity model is introduced, and design procedures of parameter estimation of online monitoring system for eccentricity-induced disturbance are proposed. In order to demonstrate the applicability and performance of the proposed system, a case study from cold rolling mills in actual industrial fields as well as simulation results are given in Section V. Finally, Section VI concludes this paper. II. G ENERAL D ESCRIPTION
OF
ROLLING M ILL S YSTEM
The key equipment in hot/cold tandem rolling mills is the finishing mill group, which usually consists of 7 mill stands in hot rolling and 5 mill stands in cold rolling. The strip passes through roll gap in each stand by physical contact with a pair of work rolls, where the work rolls are driven by electric motor from main drive system, and are supported by a pair of backup rolls of larger diameters. There are two hydraulic reduction
2
devices on each side of the top backup roll, which screw down indirectly to rolled strip via force transmission between backup rolls and work rolls. hobj +
"h
h Thickness Outer Loop ! S Sobj ! SREF
AGC
Position Inner Loop S
!
Top Backup Roll
Roll Gap Instrument
Work Rolls
h1
h2
Rolling Direction
1 C
Bottom Backup Roll P
Housing of Rolling Mill (including rolling force sensor)
Fig. 1.
The structure of mill stand with AGC system
The hydraulic reduction device is used for strip gauge control system, including mechanical parts such as servo amplifier, servo-valve, hydraulic cylinder, and electrical parts such as digital controller and sensors, so it can be defined as a typical electromechanical-hydraulic coupling system [25], as known as the automatic gauge control (AGC) system. Taking gauge meter automatic gauge control (GM-AGC) system as an example in Fig. 1, it consists of two control loop, thickness outer loop and position inner loop, where its control output is thickness variation δh and roll gap reference input SREF . The rolling force P as well as roll gap value S can be directly measured by sensors. As shown in Fig. 1, before the strip enters some finishing mill stand as thickness h1 , the roll gap has already been set to a certain value as Sobj through AGC system, based on requirement of strip specification and process parameter, and the rolling force will be established via hydraulic and rolls system at the same time. let us assume the expected strip exit thickness is hobj (hobj = h2 under ideal conditions) , which is usually greater than our original roll gap, because of the elastic deformation of the whole mill stand. This relationship also can be explained well in the following ”spring equation”: P (1) C The above equation is a generalized form, where C is the equivalent stiffness of mill stand; h is defined as actual exit thickness, and original thickness set value hobj will subtract h, to produce error δh as an input to the AGC system. Among the different control strategies of AGC system, the most widely used one in hot/cold rolling mills is GM-AGC, which is a feedback control algorithm based on spring equation. Since h=S+
0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2015.2442223, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
3
GM-AGC
Servo Hydraulic System
#PM
#PE 1 C
#hobj !
"h
Controller C2(s)
C
Q C
"S !
Controller C1(s)
#u$
Servo Amplifier G1(s)
#i
Servo Valve G2(s)
#q Hydraulic & Rolls System
#S P
#h
G3(s)
Position Sensor G4(s)
Fig. 2.
The block diagram of closed-loop gauge control system
1. rotation center of roll body; 2.rotation center of roll neck; 3.rotation center of roll body and roll neck. a) roll eccentricity(single period); b) roll eccentricity(double period); c) roll eccentricity(third period); d) roll eccentricity(actual shape) Fig. 3.
Types of backup roll eccentricity
every mill stand will pass the pre-loading experiments before its actual operation, the nonlinear relationship between S and P can be eliminated [1], then the mechanical and electrical components in GM-AGC system can run around its working points during dynamic rolling process. Based on that, the incremental model can be established in Fig. 2. where the reference input of GM-AGC, ∆hobj can be defined as zero, ∆PM , ∆PE is respectively the rolling force variation by second level model calculation and roll eccentricity-induced disturbance. The system output ∆h is expected to track ∆hobj within the influence by disturbances including roll eccentricity. There are two control loops, thickness outer loop and position inner loop (as known as automatic position controlAPC) in GM-AGC system, both with PID controllers, C1 (s) and C2 (s). And the transfer function of servo amplifier is:
where ωsv represents the equivalent natural frequency of servo valve, ξsv represents the equivalent damping ratio of servo valve. The transfer function of hydraulic and rolls system can be described by:
G1 (s) = Ka
III. ROLL E CCENTRICITY M ONITORING S YSTEM D ESIGN
(2)
After linearization around operating point, the frequency characteristics of the electro-hydraulic servo valve are usually expressed as a second-order oscillation link with its transfer function shown as follows: Ksv (3) G2 (s) = 1 2ξsv 2 ω 2 s + ωsv s + 1 sv
G3 (s) =
AP /(0.5CKce ) AP 2 s ( 0.5CK ce
2
+ 1)( ωso 2 +
2ξo ωo s
+ 1)
(4)
where Ap is the effective area of piston, ξo is the damping rate of hydraulic cylinder, Kce is the flow pressure coefficient of servo valve and ωo is the angle frequency of the secondorder oscillation system. Furthermore, the transfer function of position sensor is: G4 (s) =
1 1 + T4 s
(5)
A. Roll eccentricity model Generally speaking, all the irregularities of roll shape and roll bearings in mill stand can be defined as roll eccentricities, which will not only result in the periodic disturbances on strip thickness, but also can cause the degradation on control performance of regular AGC system. Since the backup rolls,
0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2015.2442223, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
4
work rolls and strip always remain in contact, rotating together during rolling process, and the diameter of backup roll is about three times the diameter of work roll, then the main thickness deviation due to roll eccentricity can be mainly attributed to eccentricity-induced disturbance from backup rolls. In Fig. 3, types of eccentricity of backup roll are shown. A unified model of 4-h finishing mill stand is given as: n X
e(t) =
ai cos(ωi t + ϕi ) + η(t)
(6)
i=1
where e(t) is roll eccentricity signal, n is the number of eccentricity harmonic which depends on compensation accuracy of control system, ai , ωi , ϕi are the three key parameters of eccentricity-induced disturbance which respectively represents amplitude, frequency and phase of the i-th cosine wave, where there initial values can be obtained by FFT algorithm from rolling force value during rolling pre-loading experiment. η(t) denotes the stochastic noise. The model of the eccentricity (6) is referred as one of the special form of the static sinusoidal model. Since the eccentricity signal is completely specified once the parameters of the model are known, the task is to acquire and monitor these parameters online only based on the observations. B. An adaptive observer for frequency estimation Adaptive observer is proposed to simultaneously estimate the system state variables and the unknown system parameters by processing the plant I/O measurements online. Recall that, for any system variable y(t) in a second-order system, the homogenous equation is given by: 2
dy d y + 2ζω + ω2y = 0 dt2 dt
(7)
in which, ζ denotes the system damping ratio and ω is the undamped natural frequency with units of radians/second. When the system damping ratio ζ = 0, the initial condition response of the above underdamped system is a pure cosine function, oscillating at the undamped natural frequency ω and persists for all time: y(t) = y0 cos(ωt)
(8)
Motivated by this fact, it is a straightforward way to apply an adaptive observer for the frequency estimation. For our purpose, we first convert the underdamped system (7) from continuous-time to discrete-time. The discrete-time state-space representation of the i-th underdamped system Gi (z) of (6) with the undamped natural frequency ωi and the damping ratio ζi = 0 can be formulated as follows: 0 −1 1 − cos (ωi ts ) Ai = , Bi = , 1 2 cos (ωi ts ) 1 − cos (ωi ts ) (9) T Ci = 0 1 , xi0 = −ai cos (ωi ts ) ai
in which, ts denotes the sampling period. It is evident that the response to the initial condition (ui (k) = 0) of Gi (z) is ei (k) = ai cos(ωi kts ). As a result, the parallel connection of
G1 (z), · · · , Gi (z), · · · , Gn (z) which is denoted by G(z), can be obtained as: B1 A1 · · · 0 · · · 0 .. .. .. .. .. .. . . . . . . A= 0 · · · Ai · · · 0 , B = Bi , .. . .. .. .. .. .. (10) . . . . . Bn 0 · · · 0 · · · An C = C1 · · · Ci · · · Cn , T . x0 = x10 · · · xi0 · · · xn
Clearly, the response to the initial condition (u(k) = 0) of G(z) is a summation of time-discrete cosine functions e(k) = n P ai cos(ωi kts ). It is worth to notice that, the state space
i=1
representation of G(z) (10) contains only the frequencies ω1 · · · ωn , while the amplitudes a1 · · · an and phases ϕ1 · · · ϕn are related to the initial condition x0 and the state variables. Furthermore, it can be verified that G(z) is observable if the frequencies ω1 · · · ωn are distinct, which implies that there exists a regular transformation matrix T ∈ R2n×2n such that the G(z) can be transformed into the following observer canonical form: z(k + 1) = Az z(k) + Bz u(k) (11) e(k) = Cz z(k) where
Az = T AT −1 = Cz = CT −1 =
0
0 ··· I2n−1
.. . .. . .. .
−aω
··· 0 1
, Bz = T B = b ω ,
, z0 = T x0 .
aω , bω ∈ R2n×1 are two vectors contain the unknown frequency parameters. Since only the initial condition response (u(k) = 0) is considered in our case, bω namely Bz will not be taken into our consideration. Recall a stable state observer can eliminate the effect of the initial state, an adaptive observer could thus be designed for (11) to estimate the distinct T . unknown frequency parameters ω = ω1 · · · ωn Note that zˆ(k + 1) = Az zˆ(k) + Lz (e(k) − eˆ(k)) = A¯z zˆ(k) + Q (e(k)) ω(k) in which, Lz = −aω and A¯z = Az − Lz Cz has all its eigenvalues at zero, Q (e(k)) is a matrix of known measurement e(k). The designed adaptive observer consists the following three sub-systems: • Adaptive observer: zˆ(k + 1) = A¯z zˆ(k) + Q (e(k)) ω ˆ (k) + V (k + 1) (ˆ ω (k + 1) − ω ˆ (k)) , ξ(k) = e(k) − eˆ(k) = e(k) − Cz zˆ(k) •
(12)
Auxiliary filter: V (k + 1) = A¯z V (k) + Q (y(k)) , φ(k) = Cz V (k)
0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
(13)
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2015.2442223, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
•
5
Parameter estimator of ω: (14)
Since the number of the unknown parameters ω is n, then e(k) with n distinct frequencies is sufficiently rich for the estimation which guarantees the convergence of the estimates of ω. The detailed proof of stability and the convergence property are known results in adaptive control framework and can be found e.g. in [26]–[29]. C. An adaptive algorithm for amplitude and phase estimation T ϕ1 · · · ϕn and Assume in (6) the phases ϕ = T a1 · · · an are unknown. Our the amplitudes a = objective is to use the knowledge of the frequencies ω and the measurements of e(k) to estimate ϕ and a. Since the following identity is hold: ai cos(ωi kts + ϕi ) = βi1 cos(ωi kts ) + βi2 sin(ωi kts ) in which, βi1 = ai cos(ϕi ) and βi2 = −ai sin(ϕi ). The discrete-time roll eccentricity signal can be reformulated as: e(k) =
n X
ai cos(ωi kts + ϕi ) + η(k)
i=1 T
= ρ (k)β + η(k)
(15) (16)
where ρ(k) = [cos(ω1 kts ) sin(ω1 kts ) · · · cos(ωn kts ) sin(ωn kts )] T β = β11 β12 · · · βn1 βn2
T
To this end, several estimation schemes, i.e. gradient algorithm, projection algorithm, least-square algorithm etc., can be used for the estimation of β which contains all the information about the phases ϕ and amplitudes a. Here, the normalized gradient algorithm is adopted in this paper as an example: • Residual generator: ˆ r(k) = e(k) − ρT (k)β(k) •
(17)
Parameter estimator of a and ϕ:
ˆ + 1) = β(k) ˆ β(k + γβ (k)ρT (k)r(k), µβ γβ (k) = , σβ ≥ 0, 0 < µβ < 2, σβ + ρ(k)ρT (k) q 2 (k + 1) + β ˆ2 (k + 1) , a ˆi (k + 1) = βˆi1 i2 ! ˆ βi2 (k + 1) ϕˆi (k + 1) = − arctan . βˆi1 (k + 1)
(18)
D. Quality assessment system Based on the above studies, we propose a quality assessment system in the high level to monitoring the strip quality. Since a number of the statistical process control techniques like control chart and six sigma have been proposed and applied to analyze quality problems and to improve the performance of the process [30]. In this paper, a variational control chart
AUB
Process Variable
ω ˆ (k + 1) = ω ˆ (k) + γω (k)φT (k)ξ(k), µω γω (k) = , σω ≥ 0, 0 < µω < 2 σω + φ(k)φT (k)
UB Target Value LB ALB
Time Fig. 4.
Quality assessment system
is adopted here as shown in Fig. 4, which serves as the high level quality assessment system. The center line is a desired target value of a process variable. The range between the upper bound (UB) and the lower bound (LB) indicate the range of the high quality of the process variable. If the process variable y(k) locates within this range, we say the process variable has a high quality. The range between the UB and the acceptable upper bound (AUB), and the range between the LB and the acceptable lower bound (ALB) stand for the ranges of the acceptable quality (not the best but acceptable) of the process variable. If the process variable locates within these two ranges, we say the process variable is degraded from the high quality due to some reason but still acceptable. These four bounds could be determined from some statistical consideration, or could also be defined based on expectations of the process variable or engineer experiences. Finally, the ranges outside the AUB and ALB are the ranges where the process variable is badly degraded and has a poor quality, which is unacceptable. In order to visualize and quantify the quality of the process variable y(k), a general evaluation function are defined as follows: f1 (y(k), k), y(k) ∈ [LB, U B] q(k) = f2 (y(k), k), y(k) ∈ {[ALB, LB) ∪ (U B, AU B]} f3 (y(k), k), y(k) ∈ {(−∞, ALB) ∪ (AU B, ∞)}
Normally speaking, the evaluation functions (f1 , f2 and f3 ) could be chosen by the engineers based on the knowledge and requirements of the process variable y(k) to reflect the quality of y(k). Based on the evaluation function, a performance indicator I(k) is proposed and defined as:
I(k) =
k X
q(k)
(19)
k−kw +1
in which, kw is the time window chosen by the designer. The performance indicator serves as a score value of the quality of the process variable during a time window kw , and an appropriate threshold Jq,th should be given for some corresponding maintenance actions in time to prevent higher economical loss.
0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2015.2442223, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
6
TABLE I PARAMETERS GM-AGC SYSTEM
E. Design of the roll eccentricity monitoring system Based on the estimation schemes introduced in the previous two sub-sections, the online implementation of the roll eccentricity monitoring system can be summarised in the following algorithm: Algorithm: Online Implementation of Roll Eccentricity Monitoring System ˆ Step 0: Set the initial values k = 0, zˆ(0), ω ˆ (0), β(0), ρ(0), V (0) = 0, φ(0) = 0; Step 1: Design the quality monitoring system for the thickness error y(k) and set the threshold Jq,th for the maintenance action; Step 2: Compute the performance indicator I(k) according to (19) at every sample time hit. Check whether I(k) ≥ Jq,th , if yes then do the following steps; Step 3: Compute V (k + 1), ω ˆ (k + 1) and zˆ(k + 1) according to (13),(14) and (12); Step 4: Increase k by one, receive e(k). Compute ξ(k), φ(k), r(k) according to (12), (13) and (17) respectively, and go to Step 3 until ω ˆ (k) converged ; Step 5: Formulate ρˆT (k) in (16) using ω ˆ (k) and replace ˆ +1), a ρT (k) in (17) and (18). Compute β(k ˆ(k +1), ϕ(k ˆ + 1) according to (18); Step 6: Increase k by one, receive e(k). Compute r(k) according to (17), and go to Step 5 until a ˆ(k), ϕ(k) ˆ converged. Remark: Different from the other identification procedures, the proposed adaptive identification method in sub-section III-B and III-C leads to the decoupling of nonlinearity of the identification problem. The frequency can first be identified separately, and then the identification of the amplitude and phase become much easier and lots of linear identification methods could be applied. Roughly speaking, if the system input signal has at least one distinct frequency component for each two unknown parameters, then it is sufficiently rich for the identification [27]. Since the proposed identification methods decouple the identification problem, moreover, in each procedure there are at most two unknown parameters to be determined for one distinct frequency component, the convergence of the identified parameters of the proposed methods is thus guaranteed. IV. C ASE S TUDY
AND
S IMULATION R ESULTS
To verify the feasibility and effectiveness of the roll eccentricity monitoring system, a case study is executed based on the 5th mill stand of cold rolling mill, where all the parameters comes from actual industrial fields within roll eccentricity-induced disturbance, and the proposed algorithm performance can be testified according to various situations, such as the variations of amplitude, frequency and phase, with the consideration of strip quality assessment system. A. Plant Parameter Description The last stand of a 2030mm tandem 4-h cold rolling mill is chosen as simulation plant, since the influence on strip thickness deviation by roll eccentricity is more obvious in cold
Parameters Ka Ksv ωsv
Value & Unit 8 × 10−3 6.22 × 10−2 (m3 /s · A) 594(rad/s)
ξsv
0.89
Ap Kce
0.7314(m2 ) 8.43 × 10−13 (m5 /N · s)
C ω0 ξ0 Q
543(t/mm) 652.6(rad/s) 0.213 2000t/mm
D T4
1120mm 0.025ms
∆PM ∆hobj
0 0
Descriptions Gain of servo amplifier Gain of servo valve Equivalent frequency of servo valve Equivalent damping ratio of servo valve Effective area of piston Flow pressure coefficient of servo valve Mill stand stiffness Frequency of oscillation system Damping of oscillation system Plastic stiffness coefficient of strip Diameter of back up roll Time constant of position sensor Rolling force calculation error Expected thickness deviation
rolling process, due to its higher rolling speed and thinner strip exit thickness. All the simulations are carried out in the GM-AGC close-loop system, where ∆PE is the rolling force variation by roll eccentricity, as shown in Fig. 2, in order to reflect the influence by this kind of disturbance under real working conditions. The system parameters are listed in Table I, where the rolling force error between model calculation ∆PM is assumed to be zero, and the variation of rolling force by eccentricity-induced disturbance can be derived as: PE =
C ·Q e(t) C +Q
(20)
The signal component of roll eccentricity is measured via rolling force sensor during pre-loading experiment from industrial fields, and the initial parameters as well as roll eccentricity model is obtained after standard FFT method: π π e(t) = 0.0033 cos(2πf1 ·t− )+0.0016 cos(2πf2 ·t+ ) (21) 4 3 where the frequency f1 , f2 are relative to rolling speed. In this case study, f1 = 2f2 . The initial phase angle depends on the mechanical assembly after changing the working rolls. B. Online Monitoring System Design Considering the actual parameters from last mill stand of 2030mm cold rolling mill, in the case study, the desired exit strip thickness is 1mm, and the standard product thickness error ∆h should be less than ±5µm while larger than ±6µm is considered as unqualified products under industrial requirements. The product thickness error ∆h is of great interests, and for simplicity, the evaluation function q(k) and the corresponding four bounds are simply chosen as: |∆h(k)| , ∆h(k) ∈ [−5, 5] q(k) = |∆h(k)| , ∆h(k) ∈ {[−6, −5) ∪ (5, 6]} |∆h(k)| , ∆h(k) ∈ {(−∞, −6) ∪ (6, ∞)}
For the online calculation of the proposed performance indicator I(k) in Eq. (19), the evaluation time window is chosen as tw = 20. To take the later appropriate maintenance action in time and prevent higher economical loss, we consider
0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2015.2442223, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
7
Thickness Error and its Estimation 30 10
∆h(k)
15
25
ˆ ∆h(k)
10 5 5
20
ˆ ∆h(k) and ∆h(k) (µm)
0
15
0 −5
−5 −10
10 −10 0.98
0.99
1
1.01
−15 1.02 1.62
1.625
1.63
1.635
1.64
4
1.645
1.65 4
x 10
x 10
5
0
−5
−10
Eccentricity Abnormal Change −15 0.8
1
ω Estmation 1.2
1.4
a and ϕ Estmation 1.6
1.8
2
Samples
Fig. 5.
Thickness error ∆h and its estimation
the maintenance action should be activated when two-thirds of the samples in the evaluation time window beyond the acceptable bounds. Therefore, the quality threshold is set to be Jq,th = 100. The roll eccentricity (21) under consideration contains 2 different frequencies, namely n = 2. The frequency estimator thus can be designed based on the method introduced in sub-section III-B (the sampling period is ts = 10ms). The resulting parameter estimator is: •
Adaptive observer:
−∆h(k) 0 zˆ(k + 1) = A¯z zˆ(k) + −2∆h(k) 0 0 0 α 2∆h(k) 0 ˆ 1 (k) , + 0 −4∆h(k) α ˆ 2 (k) 2∆h(k) 0 ξ(k) = ∆h(k) − 0 0 0 1 zˆ(k). •
4
x 10
Auxiliary filter: 0 0 2∆h(k) 0 , V (k + 1) = A¯z V (k) + 0 −4∆h(k) 2∆h(k) 0 φ(k) = 0 0 0 1 V (k).
•
Parameter estimator of ω: α ˆ1 (k + 1) α ˆ 1 (k) = + γω (k)φT (k)ξ(k), α ˆ2 (k + 1) α ˆ 2 (k) µω , σω ≥ 0, 0 < µω < 2, γω (k) = σω + φ(k)φT (k) q 1 ω ˆ 1 (k + 1) = ˆ 2 (k) , ˆ 21 (k) − 4α α ˆ 1 (k) + α 2 q 1 ω ˆ 2 (k + 1) = ˆ 21 (k) − 4α ˆ 2 (k) . α ˆ 1 (k) − α 2
The designed parameter estimator for the amplitude and phase is exactly the same as introduced in sub-section III-C, and thus omitted here. C. Simulation and Discussion Two situations on roll eccentricity are performed in this sub-section under the real industrial background, while the effectiveness of the proposed strip thickness quality monitoring system and the roll eccentricity monitoring system is demonstrated. As we know, the frequency of roll eccentricity has direct relationship with rolling speed, namely angular velocity of backup rolls; and the amplitude of roll eccentricity can be affected and changed due to thermal expansion or wear of rolls. Thus, those two key parameters are firstly chosen for case study based on the proposed monitoring system in Matlab/Simulink. In Fig. 7, the measured output ∆h of GM-AGC close-loop system (blue curve) by roll eccentricity-induced ˆ (pink curve),are shown disturbance, and its observed value ∆h under different working conditions. The initial parameters of roll eccentricity model Eq. (21) is added in the closeloop GM-AGC system, focus its influence on rolling force
0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2015.2442223, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
8
Performance Indicator 200 180 160
Maintenance Action
140
I(k)
120
J q,th
100 80 60
Estimated Amplitude 0.03
a ˆ1
0.02
0 1.3
X: 2.09e+004 Y: 0.02044
X: 1.401e+004 Y: 0.007226
0.01
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1 4
x 10 0.01 0.008
a ˆ2
variation. Then we can see the thickness variation by the periodic disturbance due to the lack of capacity of conventional controller on roll eccentricity-induced disturbance attenuation. Meanwhile, it is worth noting that although the thickness deviation maintains its high quality earlier than 10000 sampling points (less than ±5µm), there are other kinds of disturbances are neglected in our manuscript, which will also affect strip thickness quality. However, the thickness quality is already degraded, when the frequency and amplitude of roll eccentricity begin to change. Both frequencies in Eq. (21) decrease 20% to simulate the rolling deceleration and their amplitude increase very slow until 20000 sampling points to reflect rolls abrasion effects. As can be seen from the left sub-plot in Fig. 5, the thickness deviation becomes larger after 10000 sampling points, while the adaptive observer for frequency estimation starts to work while the performance indicator I(k) reaches the pre-defined threshold of maintenance action Jq,th = 100 around 14600 sampling points as shown in Fig. 6. After the estimated frequencies are convergent (around 16400), the adaptive estimator of amplitude and phase is then activated.
X: 2.09e+004 Y: 0.008382
0.006
X: 1.401e+004 Y: 0.003183
0.004 0.002 0 1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
Samples Fig. 8.
2.1 4
x 10
Estimated amplitude a ˆ
Fig. 7 and Fig. 8 show the online estimation performance for frequency and amplitude of roll eccentricity monitoring system. The original rotational speed of backup rolls is 188(r/ min), then the initial frequencies of roll eccentricity can be derived as 3.1Hz and 6.2Hz, so as the initial angular velocities ω1 = 2π · f1 and ω2 = 2π · f2 can be given based on Eq. (21), as 19.48(rad/s) and 38.96(rad/s). The estimated frequencies are 15.55(rad/s) and 31.10(rad/s) which is exactly 20% off its initial value. The convergence of the estimated parameters could be easily observed from Fig. 8.
40
0 0.8
1
1.2
1.4
Samples Fig. 6.
1.6
1.8
2 4
x 10
Evaluated quality q(k) and the performance indicator I(k)
ˆ ∆h(k) and ∆h(k)
20
Thickness Error and its Estimation 20 ∆h(k) ˆ ∆h(k)
10 0 −10 2.49
2.5
2.51
2.52
2.53
2.54 4
x 10
Residual Signal 10
r(k)
5 0 −5 −10 2.49
2.5
2.51
2.52
Samples Fig. 9.
Fig. 7.
Estimated frequency ω ˆ
2.53
2.54 4
x 10
Thickness error ∆h and its estimation
The other situation of roll eccentricity needed to be discussed is the change of phase, which could happen during strip throwing period. Because it is prone to cause slip effect between working roll and backup rolls at that time due to the sudden disappearance of rolling force. The consequence of this phenomenon is a new phase of roll eccentricity emerges, thus cause accuracy decrease of compensation accuracy or even
0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2015.2442223, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
9
Estimated Phase 4 3 X: 2.7e+004 Y: 1.103
ϕˆ1
2 X: 2.41e+004 Y: 0.1167
1 0 −1 2.4
2.45
2.5
2.55
2.6
2.65
2.7
2.75
2.8 4
x 10 4 3 X: 2.7e+004 Y: 2.993
ϕˆ2
2 1 0
X: 2.41e+004 Y: 1.16
−1 2.4
2.45
2.5
2.55
2.6
2.65
Samples Fig. 10.
2.7
2.75
2.8 4
x 10
Estimated phase ϕ ˆ
the failure of roll eccentricity suppression for the next strip to be rolled. In order to simulate this phenomenon and test the estimation performance of our monitoring system. The rolling speed is defined as 20% of stable rolling speed to simulate strip throwing period, meanwhile the amplitude remains constant. The phase value in Eq. (21) increases 150 and decreases 100 respectively at sampling point 25000. From Fig. 9 and 10, we can find that the estimated thickness variation ∆h converges to the measured one quickly and the residual signal approaches to zero, which shows the effectiveness of online phase estimation during different working conditions. V. C ONCLUSION In this paper, we have designed the online parameter estimation and monitoring system for roll eccentricity. The model and characteristic of roll eccentricity as well as its influence on strip exit thickness have been introduced. For the purpose of quality quantitative assessment, We have proposed a performance indicator based on product expectations or experiences of the process variable. The online monitoring system for roll eccentricity, including adaptive observer for frequency estimation, adaptive algorithm for amplitude and phase estimation based on normalized gradient algorithm, have been presented. The performance and the effectiveness of the proposed scheme are demonstrated through rolling model from industrial fields. Through the case study, several conditions of roll eccentricity are simulated and discussed, to demonstrate the feasibility of proposed monitoring system. The estimated parameters will later be used for controller design aiming at compensating the effects of the eccentricity on strip thickness. R EFERENCES [1] V.B. Ginzburg, Flat-Rolled Steel Processes. Advanced Technologies. CRC Press, 2009. [2] A. Kugi, W. Haas, K. Schlacher, K. Aistleitner, H. Frank and G.W. Rigler, “Active compensation of roll eccentricity in rolling mills,” IEEE Trans. Ind. Appl., 36(2):625–632, 2000. [3] M. Kano and Y. Nakagawa, “Data-based process monitoring, process control, and quality improvement: Recent developments and applications in steel industry,” Computers & Chemical Engineering, vol. 32, issues 1-2, pp. 12–24, 2008.
[4] S.X. Ding, S. Yin, K. Peng, H. Hao and B. Shen, “A novel scheme for key performance indicator prediction and diagnosis with application to an industrial hot strip mill,” IEEE Trans. Ind. Informat., vol. 9, pp. 2239–2247, 2013. [5] F. Serdio, E. Lughofer, K. Pichler, T. Buchegger and H. Efendic, “Residual-based fault detection using soft computing techniques for condition monitoring at rolling mills,” Information Sciences, vol. 259, pp. 304–320, 2014. [6] L. Chiang, E. Russell and R. Braatz, Fault Detection and Diagnosis in Industrial Systems. London: Springer Verlag, 2001. [7] S. Yin, X. Li, H. Gao and O. Kaynak, “Data-based techniques focused on modern industry: An overview,” IEEE Trans. Ind. Electron., vol. 62, issue 1, pp. 657–667, 2015. [8] J. Neuzil, O. Kreibich, R. Smid, “A distributed fault detection system based on IWSN for machine condition monitoring,” IEEE Trans. Ind. Informat., vol. 10, no. 2, pp. 1118–1123, 2014. [9] S. Yin, S.X. Ding, X. Xie and H. Luo, “A review on basic datadriven approaches for industrial process monitoring,” IEEE Trans. Ind. Electron., vol. 61, issue 11, pp. 6418–6428, 2014. [10] C. Abeykoon, “A novel soft sensor for real-time monitoring of the die melt temperature profile in polymer extrusion,” IEEE Trans. Ind. Electron., vol. 61, no. 12, pp. 7113–7123, 2014. [11] M. Blanke, M. Kinnaert, J. Lunze and M. Staroswiecki, Diagnosis and Fault-Tolerant Control. Springer, 2003. [12] S.X. Ding, Model-based Fault Diagnosis Techniques, 2nd Ed., Springer, 2013. [13] S. Huang, K.K. Tan and T.H. Lee, “Fault diagnosis and fault-tolerant control in linear drives using the kalman filter,” IEEE Trans. Ind. Electron., vol. 59, no. 11, pp. 4285–4292, 2012. [14] S.J. Qin, “Survey on data-driven industrial process monitoring and diagnosis,” Annual Reviews in Control, vol. 36 pp. 220–234, 2012. [15] S. Yin, H. Luo and S.X. Ding, “Real-time implementation of faulttolerant control systems with performance optimization,” IEEE Trans. Ind. Electron., vol. 64 issue 5, pp. 2402–2411, 2014. [16] S.X. Ding, Data-driven Design of Fault Diagnosis and Fault-tolerant Control Systems. Springer, 2014. [17] A. Haghani, T. Jeinsch and S.X. Ding, “Quality-related fault detection in industrial multimode dynamic processes,” IEEE Trans. Ind. Electron., vol. 61, issue 11, pp. 6446–6453, 2014. [18] X. Dai and Z. Gao, “From model, signal to knowledge: A data-driven perspective of fault detection and diagnosis,” IEEE Trans. Ind. Informat., vol. 9, issue 4, pp. 2226–2238, 2013. [19] S. Yin, X. Zhu and O. Kaynak, “Improved PLS focused on keyperformance-indicator-related fault diagnosis,” IEEE Trans. Ind. Electron., vol. 62, no. 3, pp. 1651–1658, 2015. [20] Z. Wang, K. Wang and X. Sun, “Prognosis system for roll eccentricity with MFFT based on the difference evolution algorithm,” Chinese Mechanical Engineering, 21(2): 169–173, 2010. [21] A. Bouzida, O. Touhami, R. Ibtiouen, A. Belouchrani, M. Fadel and A. Rezzoug, “Fault diagnosis in industrial induction machines through discrete wavelet transform ,” IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 4385–4395, 2011. [22] Z. Chen, F. Luo, Y. Xu, et al., “Roll eccentricity compensation based on anti-aliasing wavelet analysis method,” Journal of Iron and Steel Research International, 16(2):35–39, 2009. [23] K. Aistleitner, L.G. Mattersdorfer, W. Hass, et al., “Neural network for identification of roll eccentricity in rolling mills,” Journal of Materials Process Technology, (60):387–392, 1996. [24] D.F. Garcia, J.M. Lopez, F.J. Suarez, J. Garcia, F. Obeso and J.A. Gonzalez, “A novel real-time fuzzy-based diagnostic system of roll eccentricity influence in finishing hot strip mills,” IEEE Trans. Ind. Appl., 34(6):1342–1350, 1998. [25] X. Yang and C. Tong, “Coupling dynamic model and control of chatter in cold rolling,” Journal of Dynamic Systems, Measurement and ControlTransactions of the ASME, 134(4):1–8, 2012. [26] K.J. Astr¨om and B. Wittenmark, Adaptive Control. Addison-Wesley Publishing Company, 1995. [27] P.A. Ioannou and J. Sun, Robust Adaptive Control, Prentice-Hall, 1995. [28] Q. Zhang. “Adaptive observer for multiple-input-multiple-output (MIMO) linear time-varying systems,” IEEE Trans. Autom. Control, 47:525–529, 2002. [29] G. Tao, Adaptive Control Design and Analysis, John Wiley & Sons, 2003. [30] D.C. Montgomery, Introduction to Statistical Quality Control, Hoboken, NJ: Wiley, 2013.
0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2015.2442223, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
Xu Yang (M’12) received the B.E. degree in automation and the Ph.D degree in Control Science and Engineering from University of Science and Technology Beijing, in 2006 and 2011, respectively. He used to be a visiting scholar at the Institute for Automatic Control and Complex Systems (AKS) , University of Duisburg-Essen, Germany, from 2013 to 2014. He is currently an associate professor in the School of automation and electrical engineering, University of Science and Technology Beijing. His research interests include modeling, process monitoring, fault diagnosis and fault tolerant control system and their application in complex industrial process with a focus on hot/cold rolling mills.
10
Kaixiang Peng received the B.E. degree in automation and the M.E. and Ph.D. degree from the Research Institute of Automatic Control, University of Science and Technology, Beijing, China, in 1995, 2002 and 2007, respectively. He is a Professor with the Research Institute of Automatic Control, University of Science and Technology, Beijing, China. His research interests are fault diagnosis, prognosis, and maintenance of complex industrial processes, modeling and control for complex industrial processes, and high-performance control system design for the rolling process.
Hao Luo received his B.E. degree in electrical engineering from XiAn Jiaotong University, China, in 2007, M.Sc. degree in electrical engineering and information technology from University of DuisburgEssen, Germany, in 2012. He is currently working toward the Ph.D. degree at the Institute for Automatic Control and Complex Systems (AKS) at the University of Duisburg-Essen. His research interests include model based and data-driven fault diagnosis, fault-tolerant systems and their application on industrial systems.
Minjia Krueger received her B.E. degree in Measuring and Control from Huazhong University of Science and Technology,Wuhan, China, in 2008, M.Sc. degree in electrical engineering and information technology from University of Duisburg-Essen, Germany, in 2012. She is currently a Ph.D. student at the Institute for Automatic Control and Complex Systems (AKS) at the University of Duisburg-Essen. Her research interests include model based and datadriven fault diagnosis, and their applications on industrial processes and renewable energy systems.
Steven X. Ding received Ph.D. degree in electrical engineering from the Gerhard-Mercator University of Duisburg, Germany, in 1992. From 1992 to 1994, he was a R&D engineer at Rheinmetall GmbH. From 1995 to 2001, he was a professor of control engineering at the University of Applied Science Lausitz in Senftenberg, Germany, and served as vice president of this university during 1998 to 2000. Since 2001, he has been a professor of control engineering and the head of the Institute for Automatic Control and Complex Systems (AKS) at the University of Duisburg-Essen, Germany. His research interests are model-based and datadriven fault diagnosis, fault-tolerant systems and their application in industry with a focus on automotive systems and chemical processes.
0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
