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A novel real-time fuzzy-based diagnostic system of roll eccentricity influence in finishing hot strip mills

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1342 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 6, NOVEMBER/DECEMBER 1998
A Novel Real-Time Fuzzy-Based DiagnosticSystem of Roll Eccentricity Inﬂuencein Finishing Hot Strip Mills
Daniel F. Garc´ıa, Jos´e M. L´opez, Francisco J. Su´arez, Javier Garc´ıa, Faustino Obeso, and Juan A. Gonz´alez
Abstract—
This paper proposes a method for the diagnosis of the inﬂuence of roll eccentricity on the strip thickness at theexit of a ﬁnishing hot strip mill (FHSM). Each strip thicknessdefect on exit is related to a roll of the FHSM, allowing theimplementation of an optimal policy for the substitution andmaintenance of the rolls, thereby maintaining the required qualitylevel of the strip. This policy allows the minimization of rollchanges and the concentration of several changes at the sametime, reducing production costs. Fuzzy logic is used to comparespectra, looking for common patterns, which allows for a totallyautomated diagnostic system. Moreover, an innovative estimateof roll eccentricity based on a least-squares algorithm has beendeveloped, which provides higher accuracy than classical algo-rithms, as well as a drastic reduction in the time required toperform eccentricity tests.
Index Terms—
Roll eccentricity, strip quality.
I. I
NTRODUCTION
G
IVEN A SET OF thickness defects measured in a rolledstrip at the exit of a ﬁnishing hot strip mill (FHSM), theproblem is to diagnose the following:1) whether defects come from roll eccentricity;2) for a defect caused by roll eccentricity, which roll orrolls produced it.In the context of this paper, some aspects have to be deﬁnedmore precisely.• Only the center gauge thickness, measured in the centerof the transversal section of the strip, is considered, asdepicted in Fig 1. Therefore, ﬂatness problems in the stripare not addressed in this paper.• A thickness defect is considered a variation of centergauge thickness. Due to the periodic nature of these de-fects, they will be characterized in the frequency domainas harmonics of thickness.• A broad deﬁnition of roll eccentricity is considered,including all the irregularities in the stand which dependon the angular position of the roll. For example, for
Paper PID 98–14, presented at the 1997 Industry Applications SocietyAnnual Meeting, New Orleans, LA, October 5–9, and approved for publicationin the IEEE T
RANSACTIONS ON
I
NDUSTRY
A
PPLICATIONS
by the Metal IndustryCommittee of the IEEE Industry Applications Society. Manuscript releasedfor publication July 14, 1998.D. F. Garc´ıa, J. M. L´opez, F. J. Su´arez, and J. Garc´ıa are with the Universityof Oviedo, 33204 Gij´on, Spain.F. Obeso and J. A. Gonz´alez are with the Centro de Desarrollo, Aceralia,33480 Avil´es, Spain.Publisher Item Identiﬁer S 0093-9994(98)08101-8.Fig. 1. Center gauge thickness.
backup rolls these would include roll ovality, eccentricityof roll journals, eccentricity of rotating sleeves in the rollbearings, nonuniformity of roll peripheries, etc. [1].There are many factors which affect the thickness qualityof rolled strips [2]. Roll eccentricity is one of the mostimportant and, consequently, any action directed to removingroll eccentricity or its effects will greatly improve thicknessquality and reduce production costs.For instance, after the rolling of a strip, the mill operatorsmay ﬁnd that the thickness measured by the X-ray gauge atthe exit of the FHSM is not up to the required quality. Inthis case, the operators must diagnose which roll or rollshave produced the thickness problems. The solution is tochange the rolls in the problematic stands. The diagnosis of which roll(s) is responsible for the defects must be fast andreliable, because, meanwhile, the mill must stop production.Furthermore, analyzing the historical values of individual rollinﬂuences, it is possible to prevent future failures in thicknessquality.Apart from the diagnosis system itself, other contributionsof this paper are the following:• a new roll-eccentricity estimation algorithm which en-ables higher accuracy than that provided by classicalalgorithms, as well as high noise immunity and shortereccentricity test times;• a fuzzy-based spectra comparer which substitutes a hu-man operator in the task of comparing spectra, lookingfor common patterns.This paper begins with the general description of the diag-nostic system. Next, the main parts of the diagnostic systemare presented. Finally, the results of the diagnostic system
0093–9994/98$10.00
1998 IEEE
GARC´IA
et al.
: DIAGNOSTIC SYSTEM OF ROLL ECCENTRICITY INFLUENCE IN FHSM’S 1343
Fig. 2. A seven-stand FHSM.
and their industrial exploitation are described in their currentimplementation.II. G
ENERAL
D
ESCRIPTION OF THE
D
IAGNOSTIC
S
YSTEM
The diagnosis is based on a combination of modeling,estimation, and pattern matching techniques [3]. The key ideais to compare the thickness defects measured by the X-raygauge with the thickness defects estimated at the exit of eachstand. Estimation at each stand is necessary because X-raygauges are normally available only at the exit of the last stand.A seven-stand FHSM is depicted as a reference in Fig. 2.The comparison of defects is performed in the frequencydomain, taking advantage of the periodicity of the defectsproduced by the rolls on the strip. In this way, each defectis characterized as a harmonic of thickness represented byits amplitude and frequency (the phase is unimportant in thisapproach).A comparer of spectra based on fuzzy technology is usedfor this purpose. The comparer of spectra receives ( )spectra, being the number of stands (one spectrum of outputthickness per stand) plus one additional spectrum from theX-ray gauge. The comparer determines which roll or rollsproduced each harmonic of the spectrum calculated using theX-ray measurements. With this approach, several problemsarise. The most important ones are as follows.1) Output thickness variations at the exit of each stand arenot measurable, except for at the last stand. Therefore,an observer of output thickness variations against timeat the exit of each stand is required.2) Strip speed along a rolling may vary. This generatesspectra smearing if the spectra calculations are per-formed directly on the output thickness variations at theexit of a stand, or at the X-ray gauge. The solution is toobserve the rolled strip length at the exit of each stand.The calculations of spectra are, therefore, performed onthe thickness variations as a function of the rolled striplength, rather than as a function of time.3) The length of the rolled strip at the exit of each stand isdifferent. An eccentricity harmonic produced by standmigrates up to stand ( ), where it is reduced inamplitude. Furthermore, if the reduction of stand ( )is, for example, 2.0, the eccentricity harmonic producedby stand appears in its spectrum at a frequency thatis half of the frequency at which it appeared in thespectrum of stand ( ). This makes the comparisonof spectra difﬁcult. The solution is to stretch the lengthof the rolled strip of stands 0 to ( ) to reach thelength of the rolled strip in stand ( ), being thenumber of stands.4) The last problem is to design a fuzzy-based comparer of spectra that allows the substitution of the human operatorand, so, to build a totally automated diagnostic system.III. O
BSERVATION OF
O
UTPUT
T
HICKNESS
V
ARIATIONS
A
GAINST
T
IME
During the rolling process, an observer runs the thicknessvariation model for each stand in real time. The model wasadapted from [4] and is given by(1)All the variations, represented by , are calculated withregard to a data sample used as a reference. Normally, thisreference sample is the ﬁrst sample taken, which allows easy,on-line calculation of variations. In this model, the outputvariable is the thickness variation at the exit of a standagainst time. The model receives the following measurementsas input (see Fig. 3):force measured in the stand;screw position;rotation speed of the backup rolls;angular position of the top backup roll, work rolls, and bottom backup roll in degrees, re-spectively.In addition, the structural parameters ,, and must be adjustedfor each speciﬁc mill.stand stretch variation. It contains informa-tion about stand stiffness. It is estimatedby putting the FHSM in kiss-rolling work-ing conditions and measuring force againstscrew position.oil-ﬁlm thickness variation. It is also es-timated under kiss-rolling working condi-tions by varying the screw position and thespeed of the rolls.stand eccentricity variation. Stand eccen-tricity is deﬁned by(2)
1344 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 6, NOVEMBER/DECEMBER 1998
Fig. 3. Diagram of a stand with its principal variables.
wherestand eccentricity;distance between the rotation centers of the backuprolls in kiss-rolling conditions ;mean radius of the top backup roll;mean radius of the bottom backup roll;mean diameter of the top work roll;mean diameter of the bottom work roll.Stand eccentricity takes the eccentricity of all the rollswithin the stand into account. Neither of the classic algorithmsfor the estimation of roll eccentricity [1] provide the accuracyrequired by the observer of output thickness variations. There-fore, it was necessary to develop a new eccentricity estimator,which is presented in the next section.IV. E
STIMATION OF
S
TAND
E
CCENTRICITY
V
ARIATION
In the context of this paper, a broad deﬁnition of rolleccentricity is considered, including all the irregularities inthe stand, which are dependent on the angular position of the roll. Eccentricity can be produced by different factors,such as roll proﬁle irregularities, keys in oil-ﬁlm bearings,etc. Nevertheless, because each component of roll eccentricitydepends on the position of the roll, all the factors can be addedup for calculation purposes. For example, the eccentricity dueto the rotating sleeve of a top backup roll and the eccentricitydue to an ellipsoidal section in the same roll can be combinedto obtain an equivalent section of the roll, which takes bothsources of eccentricity into account. This equivalent sectionis assumed to have the same mean radius as the roll and ishereafter referred to as
eccentricity section
.Because it is impossible to distinguish the eccentricity of one work roll mechanically coupled to another, they aresubstituted by a single
equivalent work roll
. This equivalentwork roll is assumed to rotate at the same speed as the srcinalpair of work rolls.
Fig. 4. Roll eccentricity deﬁnitions.
Finally, after adding all the eccentricity sources and sub-stituting the work rolls for the equivalent work roll, threeeccentricity sections are obtained, one per roll.If the eccentricity section were to form a perfect circle, thenthe roll would be perfect in terms of eccentricity. Actually,however, all rolls have some kind of imperfection which mayaffect the rolling process.Roll eccentricity can be described, in a general way, as thevariation between the theoretical circular outline of the rolland the outline of the eccentricity section. If the outline of the eccentricity section of a roll is expressed as a function of radius versus angle, roll eccentricity is deﬁned as the differencebetween the radius at each point of the outline and the meanradius. Nevertheless, if the outline is expressed as a functionof diameter versus angle, roll eccentricity is deﬁned as thedifference between the diameter at each point of the outlineand the mean diameter. Both deﬁnitions of roll eccentricitygiven by (3) are depicted in Fig. 4if based on radiiif based on diameters (3)whereroll eccentricity for a given angle;angle within the roll;mean radius of the roll;
GARC´IA
et al.
: DIAGNOSTIC SYSTEM OF ROLL ECCENTRICITY INFLUENCE IN FHSM’S 1345
Fig. 5. Stand eccentricity components.
mean diameter of the roll;radius of the roll as a function of the angle;diameter of the roll as a function of the angle.Stand eccentricity was deﬁned in (2) without taking intoaccount the concept of roll eccentricity. However, a relationexists between stand eccentricity and roll eccentricity. Fig. 5and (4) show this relationship, which allows the calculation of stand eccentricity and, therefore, stand eccentricity variations,starting from the eccentricity of the rolls that make up the stand(4)where mean variables are indicated with the symbol “ ”above.Equation (4) assumes a deﬁnition of eccentricity basedon radii for backup rolls and based on diameters for theequivalent work roll. The ﬁnal conclusion from (4) is that standeccentricity can be calculated by adding the eccentricity of thetop backup roll, equivalent work roll, and bottom backup roll.The algorithm of roll eccentricity estimation requires therolls to be divided into sectors, being the number of sec-tors. Within each sector of a backup roll, the radius is assumedto be constant. Likewise, the diameter of the equivalent work roll is assumed to be constant within a sector. For example,in Fig. 5. Each sector has a number that identiﬁesit within the roll. This number is assigned starting from theangular position of the roll. The angular position of the rollscan be obtained by using proximity switches which deﬁne thebeginning of a new revolution. Integrating the angular speedbetween two subsequent revolutions gives the approximateangular position of the rolls. The approximation attained issuitable for the last stands, because speed variations duringa revolution are minimal. Nevertheless, variations in the ﬁrststands may be appreciable. The problem in the ﬁrst stands canbe solved by using encoders instead of proximity switches.The drawback in this case is a higher instrumentation cost.There are also mixed solutions, which combine an encoder forthe work rolls and one proximity switch per backup roll.The FHSM is put in kiss-rolling working conditions to carryout the eccentricity estimation, while the screw positions andthe roll speeds are forced to a constant value. Under theseconditions,(5)In addition, ﬁxing the screw position and roll speed makesoil-ﬁlm variations equal to zero in practice(6)The reason for this is the low sensibility of oil-ﬁlm thicknessdue to force variations. Data taken from an eccentricity testcarried out in a particular FHSM shows a maximum forcevariation of 40 t. The use of oil-ﬁlm thickness estimationsfor the same FHSM indicates a maximum oil-ﬁlm thicknessvariation of 3.75 m for a force variation of 40 t. This valueis much smaller than the eccentricities to be measured.Substituting (5) and (6) in (1), the equation that relates thestand stretch and the stand eccentricity is obtained(7)can be expressed as a sum of roll eccentricities asgiven in (4)(8)At any given moment, only one sector of a roll (or a pairwith the same index for the equivalent work roll) is in contactwith another roll. Therefore, it is this sector which determinesthe eccentricity of the roll at that moment.For example, in the situation of Fig. 5, sector 6 of the topbackup roll determines the eccentricity of this roll. So, it ispossible to express the roll eccentricity as follows:(9)whereBoolean variables, equal to 1 if the sector is incontact with another roll, 0 otherwise;roll eccentricity variation for the top backuproll and sector ;
1346 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 6, NOVEMBER/DECEMBER 1998
roll eccentricity variation for the equivalentwork roll and pair of sectors ;roll eccentricity variation for the bottom backuproll and sector .In the position of Fig. 5,, and the rest are zero.Substituting (9) in (8), the ﬁnal equation used for rolleccentricity estimation is obtained(10)Many samples of data are available during an eccentricitytest. Variation of stand stretch is calculated from the standforce. Coefﬁcients equal to 1 are obtained from theangular position of the rolls.In total, there are unknown quantities, one per ec-centricity variation. In theory, as many equations as unknownsare necessary, but, in practice, there are many more. Using aleast-squares algorithm, it is possible to obtain the solutionthat best matches the sampled data in terms of square error.The srcinal least-squares algorithm has been modiﬁed inorder to take advantage of the Boolean character of thevariables. For example, if the rolls are divided into 36 sectors(10 of resolution), there are 90 eccentricity values to estimate.However, for each sample of data, only three values of will not equal zero.Solving (10) by using least squares produces inﬁnite solu-tions, which only differ in the mean value of eccentricity foreach roll. For example, if isa solution of (10), thenis also a solution, being an arbitrary constant. Least-squaresalgorithms may generate any of these inﬁnite solutions. Chang-ing the eccentricity reference to a position in the rolls havingzero eccentricity, eccentricity variations coincide with rolleccentricity and (11) is applied(11)Therefore, if after applying the least-squares algorithm on(10), the result is obtained,then the correct solution to the problem of roll eccentricityestimation, , can be calculatedfrom(12)Least-squares algorithms present immunity to certain typesof noise, as described in [5], which makes these algorithmsvery suitable for industrial environments.Moreover, many classical algorithms of roll eccentricityestimation work in the frequency domain, using the beatphenomenon [1] to separate the eccentricity of the top andthe bottom backup rolls. Beat cycle is given by(13)where are the mean diameters of the top and bottombackup rolls and is the mill spee.If the diameters of the top and bottom backup rolls aresimilar (as is normally the case), the beat cycle can reachvalues in the order of minutes.The proposed eccentricity estimation algorithm requiresonly a period , times lower than to converge towardthe solution(14)because in order to distinguish their eccentricities, only asector of relative displacement between the backup rolls isnecessary. For example, this algorithm has been used to obtainthe eccentricity of typical rolls in the last stand of an FHSMwith . Only 7 s of data were necessary to completethe estimation.The number of eccentricity samples per roll can be modiﬁedby acting on the value of . Nevertheless, computationalcost, in terms of the time required to process a sample,increments approximately to a power of 2computational cost (15)where is a parameter dependent on the target computer. Forexample, the time required to process a sample of data bythe algorithm is about 2.5 ms using 18 samples per roll in anaverage workstation. This time reaches about 10 ms using 36samples per roll.V. O
BSERVATION OF
R
OLLED
S
TRIP
L
ENGTH
A
GAINST
T
IME
The speed of the strip at the exit of a stand [4], , follows(see Fig. 3)(16)

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