- Email: [email protected]
Property Prediction Using Hierarchical Regression Model Based on Calibration
Available online at w.sciencedirect.com *--#I
).I0 ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTEFWYMONh. 2010, 17(8) : 30-35
Property Prediction Using Hierarchical Regression Model Based on Calibration TAN Shuail ,
CHEN Wei-dong’ ,
WANG Fu-lil ,
CHANG Yu-qing’
(1. School of Information Science and Engineering, Northeastern University, Shenyang 110004, Liaoning, China’ 2. Baosteel Industry Inspection Co, Shanghai 201900, China)
Abstract: Redundant information and inaccurate model will greatly affect the precision of quality prediction. A multiphase orthogonal signal correction modeling and hierarchical statistical analysis strategy are developed for the improvement of process understanding and quality prediction. Bidirectional orthogonal signal correction is used to remove the structured noise in both X and Y ,which does not contribute to prediction model. The corresponding loading vectors provide good interpretation of the covariant part in X and Y. According to background, hierarchical PLS (HiPLS ) is used to build regression model of process variables and property variables. This blocking leads to two model levels: the lower level shows the relationship of variables in each annealing furnace using hierarchical PLS based on bidirectional orthogonal signal correction, and the upper level reflects the relationship of annealing furnaces. With analysis of continuous annealing line data, the production precisions of hardness and elongation are improved by comparison of previous method. Result demonstrates the efficiency of the proposed algorithm for better process understanding X and property interpretation Y. Key words: continuous annealing line; property prediction; hierarchical PLS; orthogonal signal correction
Strip annealing is an important part of cold strip process, which could recrystallize the sclerotic strip and improve the microstructure and internal quality of the strip by the recovery, recrystallization and grain growth, respectively. The internal quality of strip mainly refers to the index of chemical examination of hardness and elongation. In actual production process, the head and end of the strip are cut off and the quality of product is estimated by the internal quality information coming from the off-line experiment. It is well known that there are some time delays in the off-line experiment; the correct quality situation is learned only after the strip produced for a while. This problem makes the real-time monitoring of strip quality difficult; furthermore, it is an obstacle to the improvement of product quality and qualified rate. As the rapid development of the electronic and computer application, most of the modern industry
process equipped with complete even redundant sensing measurement which could obtain a large number of process data on-line. In continuous annealing line, much process information could be obtained, such as the mateiial of strip, parameters of cold and hot rolling, the temperature of each stage in annealing furnace, the speed of center stage and etc. Obviously, these process data contain much of information which is related to the operation situation of production process and the quality of final product. The work is of practical significance if the correlation between process data and quality could be found by means of multivariate statistical analysis. Based on the background of continuous annealing line of steel plant, the Hi-PLS ( hierarchical PLS) was used to build the hierarchical regression model of the continuous annealing line, aiming to solve the massive data and multistage of the furnace. On the low-level modeling of sub block, the original
Foundation Itemr Item Sponsored by National Natural Science Foundation of China (60774068) ; National Basic Research Program of China (2009CB320601) E-mailr tanshuaineu@yahoo. cni Rece1ve.d Date: September 1, 2009 Biqmphy:TAN Shuai(1983-1, Female, Doctor;
Property Prediction Using Hierarchical Regression Model Based on Calibration
Issue 8
data is preprocessed by the Orthogonal Signal Correction (OSC) , through which the redundant information of modeling variables is removed. The useful characteristic is extracted to build the regression model of furnace temperature and strip quality exactly.
1
Method and Theory
Hierarchical PLS The modeling and analysis based on the statistic are the hot issues in recent years. In 1983, Partial Least Squares Regression (PLS) was proposed by Wold. The main work of the PLS regression is to find out the connection between “cause” and “result” which are respectively extracted from huge amounts of correlative variables. In late 30 years, the theory, method and application of PLS regression had been developed rapidly. In 1996, the Hi-PLS was proposed by WoldC’-’’, and the PLS regression was extended to multi-level regression so as to build the regression model for the large number of variables. Hi-PLS is famous for its efficiency in the research of modeling for massive data. The PLS have proven to be very effective for the multivariable process modeling. However, too many process variables will result in jumbled model, which is difficult to analyze and interpret. It is unreliable to select a subset of original variable set to build the model by simply deleting some variablesC33,as the decrease of the variable will be accompanied with the decrease of useful information for modeling. The tile and hierarchy method of Hi-PLS could simply and efficiently solve the problem of miscellaneous variables of modeling. The process of Hi-PLS could be divided into 3 steps. In the first step, the predictor variable set is divided into several sub blocks, the variable in which is of the similar meaning. In the second step, the base model of each sub block is established and the corresponding principal component of each base model should be extracted. In the last step, the holistic regression model of principal components and the response variables can be builtC5’. The modeling principle is shown in Fig. 1.
1.1
The Hi-PLS is of strong information extraction and clear structure. The structure is composed of two parts: base model and top model. The base model refers to the inner models of each sub block which is the reflection of the correlative information of response variable. The top model refers to the model between sub blocks which reflect the correlation of sub blocks. The two regressions interpret the correlation of holistic predictor and response variables. The advantage of Hi-PLS is of clear structure; however, its disadvantages can not be neglected. First, the base models reflect the correlation of final quality Y and process information X, contained in each sub block, while the top model is built by principal component extracted from each sub block. However, the final quality is not singly determined by the process information of some sub block, but the combined action of process information of all sub blocks. As to the PLS model of some sub block, only part of quality performance is interpreted, and the response variable Y contains some information which can not be interpreted by Xi.Second, the disturbance during the process of signal collection and the redundant factor of variable selection will both generate unrelated information of final quality Y which contained in the process variable X,of sub blocks. In the process of modeling, the disturbance information which is useless will decrease the precision of model. Third, for the whole process, there would be repeating superposition in the base models which is of different sub blocks respectively related with the quality index. For the reasons above, the simple base model for sub blocks X,and quality Y will inevitably cause low Signal to Noise Ratio (SNR) and poor prediction ability. Based on the practical application background, a method of hierarchical PLS combined with OSC is applied to remove’ the redundant information respectively from both predictor and response variables in order to enhance the causality of process and quality variable. Orthogonal signal correction filters OSC is derived from the basic partial least squares projections to latent structures prediction approachc4]. The idea with the orthogonal correction method is to remove variation in X that is not correlated to Yc5-61. It can improve the prediction performance of the sequent calibration model because of 1.2
-1
PISZ
pub
Fig. 1 Schematic diagram of Hi-PLS model
31
32
Journal of Iron and Steel Research, International
the increased causal relationship between the predictor and quality variables. OSC-PLS model can be expressed explicitly in the following way. Function: max [ ( X W ) ~ ( X W ) ] s. t. (XW)TY=0 wTw=l (1) where, X is predictor variables matrix; Y is response variables matrix; w is the weight vector of X . From Eqn. ( 1 ) , OSC filter separates the structured noise in X , which is orthogonal to Y . And the score matrix T = Xw involves the large systematic variation in X . Furthermore, the filtered descriptors provide more accurate process knowledge and understanding in determining the quality performance since only key and relevant information is focused on after removal of disturbing variations. In 2002, Johan Trygg developed 02-PLS algorithm based on OSC-PLSc8-'01. Compared with OSCPLS, PLS based on two-way OSC (02-PLS) separates the structured noise in both X and Y from the joint X-Y covariation used in the prediction model. It is suitable for situations where Y also consists of much uncorrelated noise with X . 'X=T*WT+Tyl *P;l+EXy (2) Y = U cT+Uxi Q s +FXy where, Tyl PFl is orthogonal systematic variations part in X ; U x l P$l is orthogonal systematic variations part in Y . The two parts are redundant inand U * cT formation for prediction quality. T * are the useful' variation information in prediction regression modeling. Em and FXy are residual matrices. 02-PLS removes the part of the data that is not contributed to quality interpretation. Furthermore, it avoids over-fitting model.
1 . 3 Hi-PLS based on OSC For the multi-stage structure and the massive data of the annealing process, the Hi-PLS is applied to modeling. In the process of base modeling, 0 2 PLS is used to extract the principal component contained in the sub blocks which is the reflection of quality. The relation of principal component of sub blocks and the final quality can be derived by the top model regression, as shown in Fig. 2. Assuming that the practical process is divided into b sub blocks, process information of each sub block is expressed as X i . By the method of OBPLS, Ai principal components til , tiz , , tiAiare respectively extracted from the i-th base model. After finishing the top regression model for the final quality
Vol. 17
Fig. 2 Schematic diagram of 02-Hi-PJS model
and principal component of each sub block, the regression model of the whole process can be obtained. Hi-PLS based on OSC is obviously suitable for the analysis of the interactipn and relation between the quality variable and each sub block model. The steps of off-line modeling of the algorithm are summarized as follows: 1 ) The variable X is divided into b sub blocks X= [XI, X , , , xb] , according to the production period. b different base models can be got through the 02-PLS training of each sub block. xb=Tb ' w;f+Tb,yl Pzyl+Eb (3) y=ub c;f+ub,xl @,xi +Fb 2 ) The principal component matrix Tb of each sub model can be got. The formula is as follows: Tb=(xb-xb &,yl P z y l ) ' wb (4) where, wb is the weight matrix of xb; Rb,Yl is weight matrix of x b , y l part; and Pb.yl is the loading matrix of x b , y l part. 3) Building the PLS regression model for the final quality and principal component matrices of base models T B = [ T I, Tz .** , Tbl. TB=Ttop PZp +Etop
Y=Utop Q ~ , + F t o P
(5)
h
Y=TB Btop where, T,,, U , are' the scores matrices of TB, Y ; P , , Qfopare the loading matrices of TB , Y ; and B,, is the regression coefficients matrix. When online application, the new on-line process data x, is divided into b sub blocks x,,= [X,l Xnewz , X n e w b ] 9 and the principal component matrix of base model TNwBis obtained according to Eqn. (4). The result of quality prediction can be
...
h
calculated by the formula Y , ,
2 2.1
=T n c w ~ B,,
.
Illustrations and Discussion Continuous annealing line description Fig. 3 is flow diagram of the continuous annea-
Issue 8
Property Prediction Using Hierarchical Regression Model Based on Calibration
Slow cooling
Final cooling
Overaging
I
1
I
Fig. 3
Rapid cooling
I
..-,
x 8(KXJ8)I
(6) where J = J 1+ J z + " * + J 8 ( J , is the number of modeling variable which is contained in the i-th sub block). Considering that the quality of strip is not determined by the production situation of some single sampling time but the production situation of whole period, the method of average trajectory is applied to take the K average of furnace condition variable for each stage, X ( l X J ) = [ X , (1X J , ) , X 2 ( l X J Z >,--., -
x
I
Heating
I
Exhaust and heat recovery
I
Flow diagram of the continuous annealing line
ling line. Annealing furnace is an important part of continuous annealing line. T h e main processes in annealing furnace include heating, soaking, slow cooling, fast cooling, overaging, and final cooling. The inner structure of strip successively experienced the stages of grain recovery, recrystallization, grain growth, carbide precipitation etc. T h e inner quality can be well improved by the stages mentioned above. T h e time-varying variables can be constructed as data matrix X ( K X J ) ( J is the number of timevarying variables; K is the number of sampling in a roll). Based on the production situation of annealing line, the method of taking average 'trajectory according to production period is applied. T h e 8 production stages of continuous annealing line are : heating, soaking, slow cooling, reheating, 1st cooling, 1st overaging, 2nd overaging and 2nd cooling. So the variable X is divided into 8 sub blocks: X ( K x J ) = [XI ( K x J1) ( K x Jz 1 ,
,xz
Soaking
33
x 8 ( 1 J8 ) 1 (7) T h e average trajectory of each stage is used as the
modeling variable. T h e furnace's condition of each separate stage just reflects the partial quality of strip. For only the whole production situation could completely reflect the final quality of strip, the characteristic information is extracted by the method of 02-Hi-PLS, and then, the model for characteristic information and final quality variable is established.
2.2
Application and process analysis
T h e process data of 120 rolls of strip are chosen for modeling, 38 process variables are divided into 8 stages, used to modeling and the sampling frequency of variable is 1 time per second. T h e process variables are shown in Table 1. T h e main effect of annealing process is to depress the hardness of strip, at the same time, to boost up the elongation. So performance indexes are the major concerning factors, and such outputs y of prediction model is two performance indexes, hardness and elongation of strip. So the property matrix Y=[yl, yz] is composed of two elements: hardness of strip y l , and elongation of strip y z . The modeling matrix X( 120 X 38) = [XI , Xz,---, &] is got from the average trajectory of the whole roll for each stage. T h e quality data matrixY(120X 2) can be got through the off-line chemistry examination after the whole roll strip is finished. T h e HiPLS modeling includes: the base modeling for 8 sub furnace stages by the method of 02-PLS and the top modeling for principal components of different base models and final quality by the method of PLS.
-
34 '
Vol. 17
Journal of Iron and Steel Research, International
Table 1 Process variables €or continuous d i n g line Furnace section Heat Furnace ( HF)
Soak Furnace ( SF)
Slow Cooling Furnace (SCF)
1st Cooling (10
Reheating (RH) 1st Overaging (10A)
2nd Overaging (20A)
2nd Cooling (20
No.
Process variables
1 2 3 4 5
Strip temperature in H F Strip velocity in H F Furnace temperature of 1st area in H F Furnace temperature of 2nd area in H F Furnace temperature of 3rd area in H F Furnace temperature of 4th area in H F 6 7 Furnace temperature of 5th area in H F 8 Strip velocity in SF 9 Furnace temperature of 1st ares in SF 10 Furnace temperature of 2nd area in SF 11 StriD temDerature in SF 1 2 Strip velocity in SCF 13 Strip temperature in SCF 14 Furnace temperature of 1st area in SCF 15 Furnace temperature of 2nd area in SCF 16 Furnace temperature of 3rd area in SCF 17 Furnace temmrature of 4th area in SCF 18 Strip velocity in 1C 19 Strip temperature in 1C 20 Furnace temperature of 1st area in 1C 21 Furnace temperature of 2nd area in 1C 22 Furnace temperature of 3rd area in 1C 23 Strip velocity in RH 24 Strip temperature in RH 25 Furnace temperature of 1st area in 1 0 A 26 Furnace temperature of 2nd area in 1 0 A 27 Strip velocity in 1 0 A 28 Strip temperature in 1st area in 1 0 A 29 Strip temperature in 2nd area in 1 0 A 30 Strip velocity in 20A-1 31 Furnace temperature of 1st area in 20A-1 32 Furnace temperature of 2nd area in 20A-1 33 Strip velocity in 20A-2 34 Furnace temperature of 1st area in 20A-2 35 Furnace temperature of 2nd area in 20A-2 36 Strip velocity in 2C 37 Strip temperature in 2C 38 Furnace temperature of 2C
a
61.6
-
60.6
.
I
6B.61
0
6
10
16
strip roll
20
26
30
* - Real measurements; 0- Predicted values. (a) 02-Hi-PLS method; (b) OX-PLS method; (c) Conventional PLS method. Fig. 4 Hardness prediction d t s €or wing the test rolls 16.2 16.0 16.8 16.6
5
16.2
1
16.0
* '
. a 16.6 . 16.8
16.2 16.0
In the same operation condition of modeling data, the production data of 30 rolls of strip is used to verify the prediction of model. Fig. 4 and Fig. 5 show the prediction of hardness and elongation, at the same time, comparing with the traditional PLS and Hi-PLS respectively. Table 2 shows the mean square error of three methods. B y comparing the images and MSE, it is obvious
16.8 16.6 0
6
10
16 skip roll
20
26
30
* - Real measurementsi 0- Predicted values. (b) OSCPLS method; (a) 02-Hi-PLS methods (c) Conventional PLS method. Fig. 5 Elongation prediction results €or using the test rolls
Issue 8
Property Prediction Using Hierarchical Regression Model Based on Calibration
Table 2
Mean square error of three methods
Algorithm
MSE (Hardness)
MSE (Elongation)
PLS Hi-PLS 02-Hi-PLS
0.063 61 0.01968 0.008 5
0.008 9 0.006 3
0.002 1
that the 02-Hi-PLS is the most effective method. The traditional PLS does not only take the relationship of variables in some stage into consideration but also considers the relationship of different stages. As for the Hi-PLS, the uncorrelated modeling information of furnace situation and quality is not removed, the over-fitting often occurred. Comparatively speaking, the presented 02-Hi-PLS is of good prediction.
3
Conclusion
Based on the practical production of continuous annealing line and the deep research of the operation mechanism, the regression model is built by the related information of the strip quality which is extracted from large number of measurable process variables. The redundant information is removed from primary data by OSC. Then, the preprocessing data is used to built the regression model with the method of Hi-PLS and the prediction of strip quality is realized by the further study of the correlation between furnace temperature and strip quality. 'By comparing the theoretical demonstration with simulation, the results prove that the method is of practical value and
35
good application prospect. References :
c11
Wold S , Antti H , Lindgren F. Orthogonal Signal Correction of Near-Infrared Spectra [J]. Chemometrics and Intelligent Laboratory Systems, 1998, 44(1): 175. c21 Sjoblom J , Svensson 0 , Josefson M. An Evaluation of Orthogonal Signal Correction Applied to Calibration Transfer of Near Infrared Spectra [J]. Chemometrics and Intelligent Laboratory Systems, 1998, 44(1): 229. c31 Svante Wold, Nouna Kettaneh, Kjell Tjessem. Hierarchical Multiblock PLS and PC Models for Easier Model Interpretation and as an Alternative to Variable Selection [J]. J Chemometrics, 1996, lO(9): 463. c41 Stefan R, John F. Adaptive Batch Monitoring Using Hierarchical PCA [J]. Chemometrics and Intelligent Laboratory Systems, 1995. 41(1): 73. c51 Zarei K, Atabati M, Malekshabani Z. Simultaneous Spectrophotometric Determination of Iron, Nickel and Cobalt in Micellar Media by Using Direct Orthogonal Signal Correction-Partial Least Squares Method [J]. Analytica Chimica Acta, 2006, 556 (1): 247. C61 Nizai A, Yazdanipour A. Spectrophotometric Simultaneous D e termination of Nitrophenol Isomers by Orthogonal Signal Correction and Partial Least Squares [J]. J Hazardous Materials, 2007, 146(1): 421. c71 Trygg J , Wold S. Orthogonal Projections to Latent Structures (OPLS) CJ]. J Chemometrics. 2002, 16(3) : 119. C81 Gabrielsson J , Jonsson H , Airiau C. The OPLS Methodology for Analysis of Multi-Block Batch Process Data [J]. J Chemometrics, 2006, ZO(8): 362. Trygg J , Wold S. 02-PLS, A Two-Block (X-Y)Latent Variac91 ble Regression (LVR) Method With an Integral OSC Filter [J]. J Chemometrics, 2003, 17(1): 53. c101 Trygg J. 02-PLS for Qualitative and Quantitative Analysis in Multivariate Calibration [J]. J Chemometrics, 2002. 16(6) : 283.
).I0 ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTEFWYMONh. 2010, 17(8) : 30-35
Property Prediction Using Hierarchical Regression Model Based on Calibration TAN Shuail ,
CHEN Wei-dong’ ,
WANG Fu-lil ,
CHANG Yu-qing’
(1. School of Information Science and Engineering, Northeastern University, Shenyang 110004, Liaoning, China’ 2. Baosteel Industry Inspection Co, Shanghai 201900, China)
Abstract: Redundant information and inaccurate model will greatly affect the precision of quality prediction. A multiphase orthogonal signal correction modeling and hierarchical statistical analysis strategy are developed for the improvement of process understanding and quality prediction. Bidirectional orthogonal signal correction is used to remove the structured noise in both X and Y ,which does not contribute to prediction model. The corresponding loading vectors provide good interpretation of the covariant part in X and Y. According to background, hierarchical PLS (HiPLS ) is used to build regression model of process variables and property variables. This blocking leads to two model levels: the lower level shows the relationship of variables in each annealing furnace using hierarchical PLS based on bidirectional orthogonal signal correction, and the upper level reflects the relationship of annealing furnaces. With analysis of continuous annealing line data, the production precisions of hardness and elongation are improved by comparison of previous method. Result demonstrates the efficiency of the proposed algorithm for better process understanding X and property interpretation Y. Key words: continuous annealing line; property prediction; hierarchical PLS; orthogonal signal correction
Strip annealing is an important part of cold strip process, which could recrystallize the sclerotic strip and improve the microstructure and internal quality of the strip by the recovery, recrystallization and grain growth, respectively. The internal quality of strip mainly refers to the index of chemical examination of hardness and elongation. In actual production process, the head and end of the strip are cut off and the quality of product is estimated by the internal quality information coming from the off-line experiment. It is well known that there are some time delays in the off-line experiment; the correct quality situation is learned only after the strip produced for a while. This problem makes the real-time monitoring of strip quality difficult; furthermore, it is an obstacle to the improvement of product quality and qualified rate. As the rapid development of the electronic and computer application, most of the modern industry
process equipped with complete even redundant sensing measurement which could obtain a large number of process data on-line. In continuous annealing line, much process information could be obtained, such as the mateiial of strip, parameters of cold and hot rolling, the temperature of each stage in annealing furnace, the speed of center stage and etc. Obviously, these process data contain much of information which is related to the operation situation of production process and the quality of final product. The work is of practical significance if the correlation between process data and quality could be found by means of multivariate statistical analysis. Based on the background of continuous annealing line of steel plant, the Hi-PLS ( hierarchical PLS) was used to build the hierarchical regression model of the continuous annealing line, aiming to solve the massive data and multistage of the furnace. On the low-level modeling of sub block, the original
Foundation Itemr Item Sponsored by National Natural Science Foundation of China (60774068) ; National Basic Research Program of China (2009CB320601) E-mailr tanshuaineu@yahoo. cni Rece1ve.d Date: September 1, 2009 Biqmphy:TAN Shuai(1983-1, Female, Doctor;
Property Prediction Using Hierarchical Regression Model Based on Calibration
Issue 8
data is preprocessed by the Orthogonal Signal Correction (OSC) , through which the redundant information of modeling variables is removed. The useful characteristic is extracted to build the regression model of furnace temperature and strip quality exactly.
1
Method and Theory
Hierarchical PLS The modeling and analysis based on the statistic are the hot issues in recent years. In 1983, Partial Least Squares Regression (PLS) was proposed by Wold. The main work of the PLS regression is to find out the connection between “cause” and “result” which are respectively extracted from huge amounts of correlative variables. In late 30 years, the theory, method and application of PLS regression had been developed rapidly. In 1996, the Hi-PLS was proposed by WoldC’-’’, and the PLS regression was extended to multi-level regression so as to build the regression model for the large number of variables. Hi-PLS is famous for its efficiency in the research of modeling for massive data. The PLS have proven to be very effective for the multivariable process modeling. However, too many process variables will result in jumbled model, which is difficult to analyze and interpret. It is unreliable to select a subset of original variable set to build the model by simply deleting some variablesC33,as the decrease of the variable will be accompanied with the decrease of useful information for modeling. The tile and hierarchy method of Hi-PLS could simply and efficiently solve the problem of miscellaneous variables of modeling. The process of Hi-PLS could be divided into 3 steps. In the first step, the predictor variable set is divided into several sub blocks, the variable in which is of the similar meaning. In the second step, the base model of each sub block is established and the corresponding principal component of each base model should be extracted. In the last step, the holistic regression model of principal components and the response variables can be builtC5’. The modeling principle is shown in Fig. 1.
1.1
The Hi-PLS is of strong information extraction and clear structure. The structure is composed of two parts: base model and top model. The base model refers to the inner models of each sub block which is the reflection of the correlative information of response variable. The top model refers to the model between sub blocks which reflect the correlation of sub blocks. The two regressions interpret the correlation of holistic predictor and response variables. The advantage of Hi-PLS is of clear structure; however, its disadvantages can not be neglected. First, the base models reflect the correlation of final quality Y and process information X, contained in each sub block, while the top model is built by principal component extracted from each sub block. However, the final quality is not singly determined by the process information of some sub block, but the combined action of process information of all sub blocks. As to the PLS model of some sub block, only part of quality performance is interpreted, and the response variable Y contains some information which can not be interpreted by Xi.Second, the disturbance during the process of signal collection and the redundant factor of variable selection will both generate unrelated information of final quality Y which contained in the process variable X,of sub blocks. In the process of modeling, the disturbance information which is useless will decrease the precision of model. Third, for the whole process, there would be repeating superposition in the base models which is of different sub blocks respectively related with the quality index. For the reasons above, the simple base model for sub blocks X,and quality Y will inevitably cause low Signal to Noise Ratio (SNR) and poor prediction ability. Based on the practical application background, a method of hierarchical PLS combined with OSC is applied to remove’ the redundant information respectively from both predictor and response variables in order to enhance the causality of process and quality variable. Orthogonal signal correction filters OSC is derived from the basic partial least squares projections to latent structures prediction approachc4]. The idea with the orthogonal correction method is to remove variation in X that is not correlated to Yc5-61. It can improve the prediction performance of the sequent calibration model because of 1.2
-1
PISZ
pub
Fig. 1 Schematic diagram of Hi-PLS model
31
32
Journal of Iron and Steel Research, International
the increased causal relationship between the predictor and quality variables. OSC-PLS model can be expressed explicitly in the following way. Function: max [ ( X W ) ~ ( X W ) ] s. t. (XW)TY=0 wTw=l (1) where, X is predictor variables matrix; Y is response variables matrix; w is the weight vector of X . From Eqn. ( 1 ) , OSC filter separates the structured noise in X , which is orthogonal to Y . And the score matrix T = Xw involves the large systematic variation in X . Furthermore, the filtered descriptors provide more accurate process knowledge and understanding in determining the quality performance since only key and relevant information is focused on after removal of disturbing variations. In 2002, Johan Trygg developed 02-PLS algorithm based on OSC-PLSc8-'01. Compared with OSCPLS, PLS based on two-way OSC (02-PLS) separates the structured noise in both X and Y from the joint X-Y covariation used in the prediction model. It is suitable for situations where Y also consists of much uncorrelated noise with X . 'X=T*WT+Tyl *P;l+EXy (2) Y = U cT+Uxi Q s +FXy where, Tyl PFl is orthogonal systematic variations part in X ; U x l P$l is orthogonal systematic variations part in Y . The two parts are redundant inand U * cT formation for prediction quality. T * are the useful' variation information in prediction regression modeling. Em and FXy are residual matrices. 02-PLS removes the part of the data that is not contributed to quality interpretation. Furthermore, it avoids over-fitting model.
1 . 3 Hi-PLS based on OSC For the multi-stage structure and the massive data of the annealing process, the Hi-PLS is applied to modeling. In the process of base modeling, 0 2 PLS is used to extract the principal component contained in the sub blocks which is the reflection of quality. The relation of principal component of sub blocks and the final quality can be derived by the top model regression, as shown in Fig. 2. Assuming that the practical process is divided into b sub blocks, process information of each sub block is expressed as X i . By the method of OBPLS, Ai principal components til , tiz , , tiAiare respectively extracted from the i-th base model. After finishing the top regression model for the final quality
Vol. 17
Fig. 2 Schematic diagram of 02-Hi-PJS model
and principal component of each sub block, the regression model of the whole process can be obtained. Hi-PLS based on OSC is obviously suitable for the analysis of the interactipn and relation between the quality variable and each sub block model. The steps of off-line modeling of the algorithm are summarized as follows: 1 ) The variable X is divided into b sub blocks X= [XI, X , , , xb] , according to the production period. b different base models can be got through the 02-PLS training of each sub block. xb=Tb ' w;f+Tb,yl Pzyl+Eb (3) y=ub c;f+ub,xl @,xi +Fb 2 ) The principal component matrix Tb of each sub model can be got. The formula is as follows: Tb=(xb-xb &,yl P z y l ) ' wb (4) where, wb is the weight matrix of xb; Rb,Yl is weight matrix of x b , y l part; and Pb.yl is the loading matrix of x b , y l part. 3) Building the PLS regression model for the final quality and principal component matrices of base models T B = [ T I, Tz .** , Tbl. TB=Ttop PZp +Etop
Y=Utop Q ~ , + F t o P
(5)
h
Y=TB Btop where, T,,, U , are' the scores matrices of TB, Y ; P , , Qfopare the loading matrices of TB , Y ; and B,, is the regression coefficients matrix. When online application, the new on-line process data x, is divided into b sub blocks x,,= [X,l Xnewz , X n e w b ] 9 and the principal component matrix of base model TNwBis obtained according to Eqn. (4). The result of quality prediction can be
...
h
calculated by the formula Y , ,
2 2.1
=T n c w ~ B,,
.
Illustrations and Discussion Continuous annealing line description Fig. 3 is flow diagram of the continuous annea-
Issue 8
Property Prediction Using Hierarchical Regression Model Based on Calibration
Slow cooling
Final cooling
Overaging
I
1
I
Fig. 3
Rapid cooling
I
..-,
x 8(KXJ8)I
(6) where J = J 1+ J z + " * + J 8 ( J , is the number of modeling variable which is contained in the i-th sub block). Considering that the quality of strip is not determined by the production situation of some single sampling time but the production situation of whole period, the method of average trajectory is applied to take the K average of furnace condition variable for each stage, X ( l X J ) = [ X , (1X J , ) , X 2 ( l X J Z >,--., -
x
I
Heating
I
Exhaust and heat recovery
I
Flow diagram of the continuous annealing line
ling line. Annealing furnace is an important part of continuous annealing line. T h e main processes in annealing furnace include heating, soaking, slow cooling, fast cooling, overaging, and final cooling. The inner structure of strip successively experienced the stages of grain recovery, recrystallization, grain growth, carbide precipitation etc. T h e inner quality can be well improved by the stages mentioned above. T h e time-varying variables can be constructed as data matrix X ( K X J ) ( J is the number of timevarying variables; K is the number of sampling in a roll). Based on the production situation of annealing line, the method of taking average 'trajectory according to production period is applied. T h e 8 production stages of continuous annealing line are : heating, soaking, slow cooling, reheating, 1st cooling, 1st overaging, 2nd overaging and 2nd cooling. So the variable X is divided into 8 sub blocks: X ( K x J ) = [XI ( K x J1) ( K x Jz 1 ,
,xz
Soaking
33
x 8 ( 1 J8 ) 1 (7) T h e average trajectory of each stage is used as the
modeling variable. T h e furnace's condition of each separate stage just reflects the partial quality of strip. For only the whole production situation could completely reflect the final quality of strip, the characteristic information is extracted by the method of 02-Hi-PLS, and then, the model for characteristic information and final quality variable is established.
2.2
Application and process analysis
T h e process data of 120 rolls of strip are chosen for modeling, 38 process variables are divided into 8 stages, used to modeling and the sampling frequency of variable is 1 time per second. T h e process variables are shown in Table 1. T h e main effect of annealing process is to depress the hardness of strip, at the same time, to boost up the elongation. So performance indexes are the major concerning factors, and such outputs y of prediction model is two performance indexes, hardness and elongation of strip. So the property matrix Y=[yl, yz] is composed of two elements: hardness of strip y l , and elongation of strip y z . The modeling matrix X( 120 X 38) = [XI , Xz,---, &] is got from the average trajectory of the whole roll for each stage. T h e quality data matrixY(120X 2) can be got through the off-line chemistry examination after the whole roll strip is finished. T h e HiPLS modeling includes: the base modeling for 8 sub furnace stages by the method of 02-PLS and the top modeling for principal components of different base models and final quality by the method of PLS.
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34 '
Vol. 17
Journal of Iron and Steel Research, International
Table 1 Process variables €or continuous d i n g line Furnace section Heat Furnace ( HF)
Soak Furnace ( SF)
Slow Cooling Furnace (SCF)
1st Cooling (10
Reheating (RH) 1st Overaging (10A)
2nd Overaging (20A)
2nd Cooling (20
No.
Process variables
1 2 3 4 5
Strip temperature in H F Strip velocity in H F Furnace temperature of 1st area in H F Furnace temperature of 2nd area in H F Furnace temperature of 3rd area in H F Furnace temperature of 4th area in H F 6 7 Furnace temperature of 5th area in H F 8 Strip velocity in SF 9 Furnace temperature of 1st ares in SF 10 Furnace temperature of 2nd area in SF 11 StriD temDerature in SF 1 2 Strip velocity in SCF 13 Strip temperature in SCF 14 Furnace temperature of 1st area in SCF 15 Furnace temperature of 2nd area in SCF 16 Furnace temperature of 3rd area in SCF 17 Furnace temmrature of 4th area in SCF 18 Strip velocity in 1C 19 Strip temperature in 1C 20 Furnace temperature of 1st area in 1C 21 Furnace temperature of 2nd area in 1C 22 Furnace temperature of 3rd area in 1C 23 Strip velocity in RH 24 Strip temperature in RH 25 Furnace temperature of 1st area in 1 0 A 26 Furnace temperature of 2nd area in 1 0 A 27 Strip velocity in 1 0 A 28 Strip temperature in 1st area in 1 0 A 29 Strip temperature in 2nd area in 1 0 A 30 Strip velocity in 20A-1 31 Furnace temperature of 1st area in 20A-1 32 Furnace temperature of 2nd area in 20A-1 33 Strip velocity in 20A-2 34 Furnace temperature of 1st area in 20A-2 35 Furnace temperature of 2nd area in 20A-2 36 Strip velocity in 2C 37 Strip temperature in 2C 38 Furnace temperature of 2C
a
61.6
-
60.6
.
I
6B.61
0
6
10
16
strip roll
20
26
30
* - Real measurements; 0- Predicted values. (a) 02-Hi-PLS method; (b) OX-PLS method; (c) Conventional PLS method. Fig. 4 Hardness prediction d t s €or wing the test rolls 16.2 16.0 16.8 16.6
5
16.2
1
16.0
* '
. a 16.6 . 16.8
16.2 16.0
In the same operation condition of modeling data, the production data of 30 rolls of strip is used to verify the prediction of model. Fig. 4 and Fig. 5 show the prediction of hardness and elongation, at the same time, comparing with the traditional PLS and Hi-PLS respectively. Table 2 shows the mean square error of three methods. B y comparing the images and MSE, it is obvious
16.8 16.6 0
6
10
16 skip roll
20
26
30
* - Real measurementsi 0- Predicted values. (b) OSCPLS method; (a) 02-Hi-PLS methods (c) Conventional PLS method. Fig. 5 Elongation prediction results €or using the test rolls
Issue 8
Property Prediction Using Hierarchical Regression Model Based on Calibration
Table 2
Mean square error of three methods
Algorithm
MSE (Hardness)
MSE (Elongation)
PLS Hi-PLS 02-Hi-PLS
0.063 61 0.01968 0.008 5
0.008 9 0.006 3
0.002 1
that the 02-Hi-PLS is the most effective method. The traditional PLS does not only take the relationship of variables in some stage into consideration but also considers the relationship of different stages. As for the Hi-PLS, the uncorrelated modeling information of furnace situation and quality is not removed, the over-fitting often occurred. Comparatively speaking, the presented 02-Hi-PLS is of good prediction.
3
Conclusion
Based on the practical production of continuous annealing line and the deep research of the operation mechanism, the regression model is built by the related information of the strip quality which is extracted from large number of measurable process variables. The redundant information is removed from primary data by OSC. Then, the preprocessing data is used to built the regression model with the method of Hi-PLS and the prediction of strip quality is realized by the further study of the correlation between furnace temperature and strip quality. 'By comparing the theoretical demonstration with simulation, the results prove that the method is of practical value and
35
good application prospect. References :
c11
Wold S , Antti H , Lindgren F. Orthogonal Signal Correction of Near-Infrared Spectra [J]. Chemometrics and Intelligent Laboratory Systems, 1998, 44(1): 175. c21 Sjoblom J , Svensson 0 , Josefson M. An Evaluation of Orthogonal Signal Correction Applied to Calibration Transfer of Near Infrared Spectra [J]. Chemometrics and Intelligent Laboratory Systems, 1998, 44(1): 229. c31 Svante Wold, Nouna Kettaneh, Kjell Tjessem. Hierarchical Multiblock PLS and PC Models for Easier Model Interpretation and as an Alternative to Variable Selection [J]. J Chemometrics, 1996, lO(9): 463. c41 Stefan R, John F. Adaptive Batch Monitoring Using Hierarchical PCA [J]. Chemometrics and Intelligent Laboratory Systems, 1995. 41(1): 73. c51 Zarei K, Atabati M, Malekshabani Z. Simultaneous Spectrophotometric Determination of Iron, Nickel and Cobalt in Micellar Media by Using Direct Orthogonal Signal Correction-Partial Least Squares Method [J]. Analytica Chimica Acta, 2006, 556 (1): 247. C61 Nizai A, Yazdanipour A. Spectrophotometric Simultaneous D e termination of Nitrophenol Isomers by Orthogonal Signal Correction and Partial Least Squares [J]. J Hazardous Materials, 2007, 146(1): 421. c71 Trygg J , Wold S. Orthogonal Projections to Latent Structures (OPLS) CJ]. J Chemometrics. 2002, 16(3) : 119. C81 Gabrielsson J , Jonsson H , Airiau C. The OPLS Methodology for Analysis of Multi-Block Batch Process Data [J]. J Chemometrics, 2006, ZO(8): 362. Trygg J , Wold S. 02-PLS, A Two-Block (X-Y)Latent Variac91 ble Regression (LVR) Method With an Integral OSC Filter [J]. J Chemometrics, 2003, 17(1): 53. c101 Trygg J. 02-PLS for Qualitative and Quantitative Analysis in Multivariate Calibration [J]. J Chemometrics, 2002. 16(6) : 283.