- Email: [email protected]
Application of neural-network for improving accuracy of roll-force model in hot-rolling mill
Control Engineering Practice 10 (2002) 473–478
Application of neural-network for improving accuracy of roll-force model in hot-rolling mill Dukman Leea,*, Yongsug Leeb a
Instrumentation and Control Research Group, Technical Research Laboratories, Pohang Iron & Steel Co., Ltd., Pohang 790-785, South Korea b Hot Rolling Department, Pohang Iron & Steel Co., Ltd., Pohang 790-785, South Korea Received 2 April 2001; accepted 13 August 2001
Abstract In this paper, a long-term learning method using neural-network is proposed to improve the accuracy of rolling-force prediction in hot-rolling mill. The statistical analysis shows that the overall thickness accuracy at the first-coil of the lot was very low compared to that of non-first coils. Frequent lot changes from the various product ranges make the conventional short-term learning insufficient to compensate the thickness error at this point. Thus, to solve this problem, a corrective neural-network is trained to predict the rolling force for the first coil and the conventional learning output is used for the remaining coils of the lot. By doing so, the thickness error at the head-end part of the strip is considerably reduced. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Neural network; Rolling force; Short-term learning; Long-term learning
1. Introduction In steel-making process, the finishing-mill rolling is a process of making thin steel strip from thick slab which has been produced by continuous casting. A typical process as shown in Fig. 1 consists of six or seven rolling stands where the attached rolls are used to press the steel strip. The operation of the finishing rolling is as follows. After a slab is reheated to recrystallization temperature in the furnace, it is reduced in several passes in the roughing mill before being rolled to proper dimensions in the finishing mill. During this kind of operation, the microstructure of the rolled strip becomes minute from the high-rolling force, and the strength and the toughness of the strip are also improved. The process control system of finishing mill is shown in Fig. 2. The control procedure can be divided into three stages: pre-calculation stage, real-time control stage and post-calculation stage. These are iterated per every rolling sequences: pre-calculation, rolling, postcalculation in this order. In the pre-calculation stage, the controller reference values such as work roll speeds, roll-gaps, strip tension,
etc. are determined from the process models before the strip arrives at the first stand of the system, which is generally called pre-setting of mill parameters. In real-time control stage, the automatic gauge controller (AGC) controls the roll gap to meet the target thickness for the strip. Fig. 3 shows thickness error signal of a strip from the thickness sensor which is normally located in the delivery side of the last stand. However, a big negative peak is obtained around 22 s and this is normally continued up to about 10–20 m in length from the starting point of the strip (this corresponds to the head-end part of the strip). The occurrence of this error is related with the improper initial roll gap setting by pre-calculation stage. On the other hand, the thickness error in the middle part of the
*Corresponding author. Tel.: +82-54-220-6295; fax: +82-54-2206914. E-mail address: [email protected] (D. Lee). 0967-0661/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 1 ) 0 0 1 4 3 - 5
Fig. 1. Configuration of finishing mill.
D. Lee, Y. Lee / Control Engineering Practice 10 (2002) 473–478
474 1
Desired Values
3
Pre-Calculation
Post-Calculation Model Adaptation
Process Models Data Base
Actual Data Collecting
Presetting
2
Real-Time Control
Automatic Gauge Control (AGC), Automatic Shape Control(ASC), etc.
Fig. 2. Process control system of rolling mill. Actual thickness : [ 2.0x977.0 mm2, 662.4 mpm] 150
100
Thickness error [um]
50
0
_
_
_
50
100
150
0
20
40
60
80
100
120
Time [sec]
Fig. 3. Thickness error trend of a rolled strip.
strip is bound within 750 mm which is considered as a good accuracy. Once actual thickness feedback is available, the thickness controller (AGC) can maintain the error small as shown in Fig. 3. Therefore, the reduction of the thickness error at the head-end part of the strip is now becoming one of the hot issues to be solved. After a rolling is finished, the post-calculation stage comes. In this stage, various model parameters are adjusted to compensate model errors by learning procedure. The process model of the pre-calculation stage consists of several sub-models to describe metallurgical, physical, thermal, and mechanical phenomena. Among them, the rolling-force model is very important because the roll-gap pre-set values are calculated from it and this determines the degree of thickness error at the head-end part of the strip. However, it is very difficult to get the correct pre-set rolling-force value from the mathematical model itself since many non-linear, unmeasurable data such as friction coefficient, yield stress, disturbances, etc. exist. To overcome these difficulties, the post-calculation stage generally adopts pass-by-pass learning scheme which is called short-term learning. Frequent lot changes due to the various products
scheduling decrease the accuracy of the learning especially in the first-coil of the lot, where the lot denotes a bunch of coils, whose size and components are similar. The neural-network is well known to have the capability of supporting or even replacing mathematical models. They adopt a non-linear mapping method to establish models according to input and output data directly; no prior knowledge of the object is needed. In this respect, many research activities to improve the rolling-force prediction were made in the past 10 years (Yamashita, Yarita, Abe, Mikuriya, & Yanagishima, 1987; Lee, 1994; Portmann, 1995; Pican, Alexandre, & Bresson, 1996; Cho, Cho, & Yoon, 1997; Lu et al., 1998). Their results can be summarized as follows. First, the use of neural-network improves the accuracy of rolling-force prediction. Secondly, those factors that cannot be considered in the mathematical model can easily be incorporated in neural-network. Thirdly, neural-network can either predict the rolling force directly or produce a corrective coefficient to be multiplied to the prediction of the mathematical model. Lastly, the use of a novelty detector improves the accuracy (Cho et al., 1997). In this paper, the rolling-force prediction is determined by multiplying the neural-network output and the rolling-force model output. Unlike the previous studies, the proposed method is the hybrid-type algorithm: at the first-coil of the lot, the neural-network compensation is applied instead of using the conventional learning output. From second to last coils in a lot, the conventional learning output is used. This scheme has merits which include least modification of existing algorithm, easy neural-network training and stable operations. The proposed neural-network is running on-line at POSCO No. 1 Hot-strip mill since July 1, 1999. This paper is organized as follows. Section 2 introduces the rolling-force model and roll-gap setting, the learning scheme, and the result of statistical analysis. Section 3 gives the result of neural-network application in rolling-force prediction. Section 4 concludes this paper.
2. Conventional method of finishing-mill setup In this section, the process model is introduced and the conventional method of finishing-mill setup (FSU) procedure is explained. 2.1. Pre-calculation First, the rolling force is predicted using the rollingforce model RF ¼ Km B Ld Qp ;
ð1Þ
D. Lee, Y. Lee / Control Engineering Practice 10 (2002) 473–478
where RF is the rolling-force model output computed from mathematical model, Km is the mean yield stress, B is the strip width, Ld is the roll contact length and Qp is the geometric term. Actually, RF is the non-linear function of the strip temperature, chemical components, thickness, width, rolling speed, etc. Next, the rolling-force prediction RFr is determined as follows: RFr ¼ ð1 þ xcl ðtÞÞRFm ;
ð2Þ
where, xcl ðtÞ is the learning coefficient of rolling-force ratio which will be defined later and RFm is the rollingforce model output calculated from Eq. (1) using the desired rolling parameters. The expected mill stretch Ms from this rolling force is given as RFr Ms ¼ ; ð3Þ M where M is the mill spring constant. Finally, if the rolling-force prediction is given, then the setup of roll-gap reference value is determined as follows: Sd ¼ h Ms þ Gm ;
ð4Þ
where Sd is the roll-gap reference value, h is the desired strip thickness, Gm is the gauge meter error compensation. 2.2. Post-calculation The rolling-force model contains many inherent errors caused by the simplified model structure, the identification errors, disturbances, etc. Especially, the system identification procedure largely resorts to the regression method, but if there are unmeasurable variables they cause a bad effect on identification accuracy. Although variables are all measurable, the measurement error makes it difficult to get the correct parameters. To reduce the errors caused from this kind of model uncertainty, learning scheme is normally used. The learning algorithm can improve the predictability of rolling force irrespective of the change of working conditions and the aging of rolling systems. For this purpose, the short-term learning and the long-term learning are normally used. Popular form of short-term learning is the exponential smoothing filter type and this is performed at every rolling pass in a lot. The running flow of it is as follows. First, it calculates the ratio of actual rolling force RFa to rolling-force model output RFma which is the recalculated force from mathematical model using actual data. Then, this rolling-force ratio is filtered and stored to be used for the next rolling pass. New learning coefficient
xcl ðtÞ of rolling-force ratio is determined as RFa 1 ; xcl ðtÞ ¼ ð1 aÞxcl ðt 1Þ þ a RFma
475
ð5Þ
where xcl ðt 1Þ is the old learning coefficient of rollingforce ratio, and a is the real value and 0pap1: On the contrary, the long-term learning is a learning scheme that uses the rolling-force ratio, which is selected after several data processing from the large number of data in the same class of the strip. Long-term learning includes any batch learning techniques such as least squares, neural-network, gain scheduling, etc. The short-term learning is aimed at compensating the inherent model error of rolling material such as yield stress errors in the same lot. However, frequent lot change from large product ranges makes it difficult to maintain a good compensation. Thus, to support the function of short-term learning, hybrid-type learning scheme that combines the long-term learning and the short-term learning simultaneously is popular these days. 2.3. Statistical analysis The results of conventional short-term learning are analyzed using 23,000 rolling data. Predictive ability of model (PAM) and predictive ability of setup (PAS) are introduced to compare the accuracy of rolling-force prediction as follows (Poliak et al., 1998). Hereafter, note that most of the statistical values are calculated from data sampled at head-end part of the strip. NCR PAM ¼ 100; TP where NCR is the number of correct predictions, TP is the total number of predictions and the correct prediction, CR, is defined as RFa RFma ð1 þ xcl ðtÞÞ p0:1: CR ¼ RF a
NCR 100; TP where the correct prediction in this case is defined as RFa RFr p0:1: CR ¼ RF PAS ¼
a
PAM shows model accuracy, whereas PAS shows prediction accuracy. Fig. 4 shows the relationship between current rollingforce model output and the actual rolling force, where xaxis and y-axis represent RFa and RFma ; respectively. The upper and lower lines represent 10% deviation from the centerline. As shown in Fig. 4, large variations and positive offset values of prediction error clearly show
D. Lee, Y. Lee / Control Engineering Practice 10 (2002) 473–478
476
Data source: 990531_990630(11090 coils) in No. 1 HSM, Pohang Works 1400
1200
1200
Recalculated rollng force [ton]
Output of roll force model with actual value [ton]
Data source: 990531_990630(11090 coils) in No. 1 HSM, Pohang Works 1400
1000
800
600
400
200 200
1000
800
600
400
400
600
800
1000
1200
200 200
1400
400
600
Measured rolling force [ton]
800 1000 Measured rolling force [ton]
Fig. 6. Relation between RFa and 89:8377%; and hit rate ¼ 82:4346%:
Fig. 4. Relation between RFa and RFma :
1200
1400
RFma ð1 þ xcl ðtÞÞ: PAM ¼
Data source: 990531_990630(11090 coils) in No. 1 HSM, Pohang Works 1400
Table 1 Comparison between first and non-first coils
FSU setup rollng force [ton]
1200
1000
Order
PAM (%)
PAS (%)
Hit rate (%)
First Non-first
80.94 94.44
64.10 79.66
69.57 89.09
800
Data source: 990531_990630(11090 coils) in No. 1 HSM, Pohang Works 1400 600
non first coils of each lot first coils of each lot 1200
200 200
400
600
800 1000 Measured rolling force [ton]
Fig. 5. Relation between RFa hit rate ¼ 82:4346%:
1200
1400
and RFr : PAS ¼ 74:3553%; and
that the rolling-force model has more inherent errors in itself. However, if the correction term from short-term learning is applied to rolling-force model output, then the prediction ability is considerably improved as shown in Figs. 5 and 6. Fig. 5 shows the relation between FSU predicted rolling force RFr and measured rolling force RFa : Fig. 6 shows the relation between recalculated rolling force RFma ð1 þ xcl ðtÞÞ and measured rolling force RFa ; where hit rate means the percentage of coils of which strip thickness error falls within 750 mm: The difference between PAS and PAM comes from the external disturbances. Next, collected data are sorted into first and non-first coils in the lot, and corresponding PAM, PAS and hit rate are calculated as shown in Table 1.
Recalculated rollng force [ton]
400
1000
800
600
400
200 200
400
600
800 1000 Measured rolling force [ton]
1200
1400
Fig. 7. Comparison between first and non-first coils.
Recalculated rolling forces RFma ð1 þ xcl ðtÞÞ at first coil ( symbol) and non-first coils ( symbol) are displayed in Fig. 7: a large number of symbols move out of 10% error lines. Both Fig. 7 and Table 1 show that the first rolling coils of the lot have a lower prediction ability than that of non-first coils. These results clearly reflect that the performance of the shortterm learning is good at compensating the thickness errors from the second coils of the lot. However, the big
D. Lee, Y. Lee / Control Engineering Practice 10 (2002) 473–478
error in the first coil shows the limitation of short-term learning.
477
follows: RFr ¼ ð1 þ xnn ðtÞÞRFm : While, for the remaining coils, the rolling-force prediction is determined using the conventional short-term learning output xcl ðtÞ as follows:
3. Long-term learning with neural network and applications
RFr ¼ ð1 þ xcl ðtÞÞRFm : The limitation of conventional short-term learning lies in its use of the one-step previous xcl ðt 1Þ in Eq. (5). Within the same lot, xcl ðt 1Þ is updated so that it compensates for the newest model error after rolling. However, xcl ðt 1Þ just after lot change is not updated because rolling is not done. Then, it contains past compensation value of model error and when this is not proper for current rolling, it can lead to large rollingforce prediction error after lot change. To cope with the limitation of conventional shortterm learning, this paper suggested a long-term learning scheme using neural-network (see Fig. 8). By using the good non-linear mapping capability of neural-network, it is trained to fully learn the model error at specific input conditions. Since neural-network compensation is not directly affected by previous xcl ðt 1Þ; the accuracy of rolling-force prediction can be maintained high, irrespective of lot changes. For implementation purpose, neural-network compensation is applied at the first coil after lot change, while conventional short-term learning output is used for remaining coils of the lot. The design of neural-network is done as follows. The neural-network is trained to map the non-linear function RFa =RFma 1: After training, the prediction of rolling force is performed as follows. For the first-coil of the lot, the rolling-force prediction is done using the neural-network output xnn ðtÞ as
According to our simulation, the combination method (multiply or addition type) of the neural-network and the mathematical model does not affect the results much. From the several simulation tests, one hidden layer for the neural-network is selected and the tangential sigmoid function is used as non-linear function of neuron. The input parameters are determined by considering the mathematical model inputs and engineers’ experiences. The selected 16 inputs are as follows: xðt 1Þ; RFm ; target strip thickness, target strip width, work roll speed, temperature, C, Mn, Si, B, Mo, Ti, Nb, Cr, furnace duration time, and furnace number. Among them, C, Mn, Si, B, Mo, Ti, Nb and Cr are the chemical components. Especially, since furnace number and furnace duration time highly affect the rolling conditions in our target system, they are used as neuralnetwork input. All input variables are normalized as follows: x mx x# ¼ ; sx where x is the input variable, mx is the mean value of input variable, and sx is the standard deviation. For training, about 15,000 coils are selected and Levenberg–Marquardt back-propagation algorithm (Hagan & Menhaj, 1994) is used.
eoff =
Off-line Learning (Long Term) ξ NN NN1 (1 + ξ NN ) Σ
RFa −1 RFma
Calc. Error2
1 Rolling Conditions
MM
Π
f(...)
RFr
ξ CL CL
RFm
RFa SDr
(1 + ξ CL )
Σ
Scr ew Down Calc. e =
PLANT Calc. Error1
Actual Data
MM RFa
on RFma 1 On-line Learning (Short Term)
RFma
−1
RFr = (1 + ξ NN ) RFm (For First Coil) RFr = (1 + ξ CL ) RFm (For Non First Coil)
ξ CL (t + 1) = (1 − α )ξ CL (t ) + αeon (Short Term Learning) Fig. 8. Block diagram of neural-network application.
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D. Lee, Y. Lee / Control Engineering Practice 10 (2002) 473–478
Conventional
Proposed
Fig. 9. On-line test results at first coils.
With the neural-network long-term learning, PAM is increased by 6.2% and hit rate by 2.1% in no. 6-stand. The averaged thickness error and standard deviation decrease by 7.3 and 2:2 mm; respectively (see Fig. 9). In the case of number 5 stand, hit rate and averaged thickness errors, standard deviation improve by 3.2%, 9.4, 2:4 mm; respectively. In addition, this improvement increased the overall thickness accuracy of the strip.
4. Conclusion In this paper, a long-term learning method using neural-network is proposed to improve the accuracy of rolling-force prediction in hot-rolling mill. From the statistical analysis, it is found that severe thickness error exists in the first-coil of the lot and the conventional learning scheme is not useful to compensate the error at this point. Thus, to solve this problem, neural-network method is combined with the conventional learning algorithm in the pre-calculation stage. By doing so, considerable thickness improvements are obtained in Pohang No. 1 hot strip mill of the Republic of Korea. However, in order to adapt the neural-network properly to process variations, its training needs to be done periodically with a large number of data. Current weight update is done off-line, while the procedures such as data gathering, filtering, training, checking, etc. can
be a burden to the operator. Thus, for ease of maintenance and effectiveness, of neural-network training method, an update of its weight in online is considered as the topic of future study.
References Cho, S., Cho, Y., & Yoon, S. (1997). Reliable roll force prediction in cold mill using multiple neural networks. IEEE Transactions on Neural Networks, 8, 874–882. Hagan, M. T., & Menhaj, M. B. (1994). Training feedforward networks with the marquardt algorithm. IEEE Transactions on Neural Networks, 5, 989–993. Lee, W. (1994). Improvement of set-up model for tandem cold rolling mill. Technical Report, RIST. Lu, C. et al. (1998). Application of ann in combination with mathematical models in prediction of rolling load of the finishing stands in hsm. Proceedings of Steel Rolling, vol. 98 (pp. 206–209). Pican, N., Alexandre, F., & Bresson, P. (1996). Artificial neural networks for the presetting of a steel temper mill. IEEE Expert, 11, 22–27. Poliak, E. I., et al. (1998). Application of linear regression analysis in accuracy assessment of rolling-force calculations. Metals and Materials, 4, 1047–1056. Portmann, N. F. (1995). Application of neural networks in rolling mill automation. Iron and Steel Engineer, 33–36. Yamashita, M., Yarita, I., Abe, H., Mikuriya, T., Yanagishima, F. (1987). Technologies of flying gauge change in fully continuous cold rolling mill for thin gauge steel strips. IRSID Rolling Conference, vol. 2 (pp. E.36.1–E.36.11).
Application of neural-network for improving accuracy of roll-force model in hot-rolling mill Dukman Leea,*, Yongsug Leeb a
Instrumentation and Control Research Group, Technical Research Laboratories, Pohang Iron & Steel Co., Ltd., Pohang 790-785, South Korea b Hot Rolling Department, Pohang Iron & Steel Co., Ltd., Pohang 790-785, South Korea Received 2 April 2001; accepted 13 August 2001
Abstract In this paper, a long-term learning method using neural-network is proposed to improve the accuracy of rolling-force prediction in hot-rolling mill. The statistical analysis shows that the overall thickness accuracy at the first-coil of the lot was very low compared to that of non-first coils. Frequent lot changes from the various product ranges make the conventional short-term learning insufficient to compensate the thickness error at this point. Thus, to solve this problem, a corrective neural-network is trained to predict the rolling force for the first coil and the conventional learning output is used for the remaining coils of the lot. By doing so, the thickness error at the head-end part of the strip is considerably reduced. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Neural network; Rolling force; Short-term learning; Long-term learning
1. Introduction In steel-making process, the finishing-mill rolling is a process of making thin steel strip from thick slab which has been produced by continuous casting. A typical process as shown in Fig. 1 consists of six or seven rolling stands where the attached rolls are used to press the steel strip. The operation of the finishing rolling is as follows. After a slab is reheated to recrystallization temperature in the furnace, it is reduced in several passes in the roughing mill before being rolled to proper dimensions in the finishing mill. During this kind of operation, the microstructure of the rolled strip becomes minute from the high-rolling force, and the strength and the toughness of the strip are also improved. The process control system of finishing mill is shown in Fig. 2. The control procedure can be divided into three stages: pre-calculation stage, real-time control stage and post-calculation stage. These are iterated per every rolling sequences: pre-calculation, rolling, postcalculation in this order. In the pre-calculation stage, the controller reference values such as work roll speeds, roll-gaps, strip tension,
etc. are determined from the process models before the strip arrives at the first stand of the system, which is generally called pre-setting of mill parameters. In real-time control stage, the automatic gauge controller (AGC) controls the roll gap to meet the target thickness for the strip. Fig. 3 shows thickness error signal of a strip from the thickness sensor which is normally located in the delivery side of the last stand. However, a big negative peak is obtained around 22 s and this is normally continued up to about 10–20 m in length from the starting point of the strip (this corresponds to the head-end part of the strip). The occurrence of this error is related with the improper initial roll gap setting by pre-calculation stage. On the other hand, the thickness error in the middle part of the
*Corresponding author. Tel.: +82-54-220-6295; fax: +82-54-2206914. E-mail address: [email protected] (D. Lee). 0967-0661/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 1 ) 0 0 1 4 3 - 5
Fig. 1. Configuration of finishing mill.
D. Lee, Y. Lee / Control Engineering Practice 10 (2002) 473–478
474 1
Desired Values
3
Pre-Calculation
Post-Calculation Model Adaptation
Process Models Data Base
Actual Data Collecting
Presetting
2
Real-Time Control
Automatic Gauge Control (AGC), Automatic Shape Control(ASC), etc.
Fig. 2. Process control system of rolling mill. Actual thickness : [ 2.0x977.0 mm2, 662.4 mpm] 150
100
Thickness error [um]
50
0
_
_
_
50
100
150
0
20
40
60
80
100
120
Time [sec]
Fig. 3. Thickness error trend of a rolled strip.
strip is bound within 750 mm which is considered as a good accuracy. Once actual thickness feedback is available, the thickness controller (AGC) can maintain the error small as shown in Fig. 3. Therefore, the reduction of the thickness error at the head-end part of the strip is now becoming one of the hot issues to be solved. After a rolling is finished, the post-calculation stage comes. In this stage, various model parameters are adjusted to compensate model errors by learning procedure. The process model of the pre-calculation stage consists of several sub-models to describe metallurgical, physical, thermal, and mechanical phenomena. Among them, the rolling-force model is very important because the roll-gap pre-set values are calculated from it and this determines the degree of thickness error at the head-end part of the strip. However, it is very difficult to get the correct pre-set rolling-force value from the mathematical model itself since many non-linear, unmeasurable data such as friction coefficient, yield stress, disturbances, etc. exist. To overcome these difficulties, the post-calculation stage generally adopts pass-by-pass learning scheme which is called short-term learning. Frequent lot changes due to the various products
scheduling decrease the accuracy of the learning especially in the first-coil of the lot, where the lot denotes a bunch of coils, whose size and components are similar. The neural-network is well known to have the capability of supporting or even replacing mathematical models. They adopt a non-linear mapping method to establish models according to input and output data directly; no prior knowledge of the object is needed. In this respect, many research activities to improve the rolling-force prediction were made in the past 10 years (Yamashita, Yarita, Abe, Mikuriya, & Yanagishima, 1987; Lee, 1994; Portmann, 1995; Pican, Alexandre, & Bresson, 1996; Cho, Cho, & Yoon, 1997; Lu et al., 1998). Their results can be summarized as follows. First, the use of neural-network improves the accuracy of rolling-force prediction. Secondly, those factors that cannot be considered in the mathematical model can easily be incorporated in neural-network. Thirdly, neural-network can either predict the rolling force directly or produce a corrective coefficient to be multiplied to the prediction of the mathematical model. Lastly, the use of a novelty detector improves the accuracy (Cho et al., 1997). In this paper, the rolling-force prediction is determined by multiplying the neural-network output and the rolling-force model output. Unlike the previous studies, the proposed method is the hybrid-type algorithm: at the first-coil of the lot, the neural-network compensation is applied instead of using the conventional learning output. From second to last coils in a lot, the conventional learning output is used. This scheme has merits which include least modification of existing algorithm, easy neural-network training and stable operations. The proposed neural-network is running on-line at POSCO No. 1 Hot-strip mill since July 1, 1999. This paper is organized as follows. Section 2 introduces the rolling-force model and roll-gap setting, the learning scheme, and the result of statistical analysis. Section 3 gives the result of neural-network application in rolling-force prediction. Section 4 concludes this paper.
2. Conventional method of finishing-mill setup In this section, the process model is introduced and the conventional method of finishing-mill setup (FSU) procedure is explained. 2.1. Pre-calculation First, the rolling force is predicted using the rollingforce model RF ¼ Km B Ld Qp ;
ð1Þ
D. Lee, Y. Lee / Control Engineering Practice 10 (2002) 473–478
where RF is the rolling-force model output computed from mathematical model, Km is the mean yield stress, B is the strip width, Ld is the roll contact length and Qp is the geometric term. Actually, RF is the non-linear function of the strip temperature, chemical components, thickness, width, rolling speed, etc. Next, the rolling-force prediction RFr is determined as follows: RFr ¼ ð1 þ xcl ðtÞÞRFm ;
ð2Þ
where, xcl ðtÞ is the learning coefficient of rolling-force ratio which will be defined later and RFm is the rollingforce model output calculated from Eq. (1) using the desired rolling parameters. The expected mill stretch Ms from this rolling force is given as RFr Ms ¼ ; ð3Þ M where M is the mill spring constant. Finally, if the rolling-force prediction is given, then the setup of roll-gap reference value is determined as follows: Sd ¼ h Ms þ Gm ;
ð4Þ
where Sd is the roll-gap reference value, h is the desired strip thickness, Gm is the gauge meter error compensation. 2.2. Post-calculation The rolling-force model contains many inherent errors caused by the simplified model structure, the identification errors, disturbances, etc. Especially, the system identification procedure largely resorts to the regression method, but if there are unmeasurable variables they cause a bad effect on identification accuracy. Although variables are all measurable, the measurement error makes it difficult to get the correct parameters. To reduce the errors caused from this kind of model uncertainty, learning scheme is normally used. The learning algorithm can improve the predictability of rolling force irrespective of the change of working conditions and the aging of rolling systems. For this purpose, the short-term learning and the long-term learning are normally used. Popular form of short-term learning is the exponential smoothing filter type and this is performed at every rolling pass in a lot. The running flow of it is as follows. First, it calculates the ratio of actual rolling force RFa to rolling-force model output RFma which is the recalculated force from mathematical model using actual data. Then, this rolling-force ratio is filtered and stored to be used for the next rolling pass. New learning coefficient
xcl ðtÞ of rolling-force ratio is determined as RFa 1 ; xcl ðtÞ ¼ ð1 aÞxcl ðt 1Þ þ a RFma
475
ð5Þ
where xcl ðt 1Þ is the old learning coefficient of rollingforce ratio, and a is the real value and 0pap1: On the contrary, the long-term learning is a learning scheme that uses the rolling-force ratio, which is selected after several data processing from the large number of data in the same class of the strip. Long-term learning includes any batch learning techniques such as least squares, neural-network, gain scheduling, etc. The short-term learning is aimed at compensating the inherent model error of rolling material such as yield stress errors in the same lot. However, frequent lot change from large product ranges makes it difficult to maintain a good compensation. Thus, to support the function of short-term learning, hybrid-type learning scheme that combines the long-term learning and the short-term learning simultaneously is popular these days. 2.3. Statistical analysis The results of conventional short-term learning are analyzed using 23,000 rolling data. Predictive ability of model (PAM) and predictive ability of setup (PAS) are introduced to compare the accuracy of rolling-force prediction as follows (Poliak et al., 1998). Hereafter, note that most of the statistical values are calculated from data sampled at head-end part of the strip. NCR PAM ¼ 100; TP where NCR is the number of correct predictions, TP is the total number of predictions and the correct prediction, CR, is defined as RFa RFma ð1 þ xcl ðtÞÞ p0:1: CR ¼ RF a
NCR 100; TP where the correct prediction in this case is defined as RFa RFr p0:1: CR ¼ RF PAS ¼
a
PAM shows model accuracy, whereas PAS shows prediction accuracy. Fig. 4 shows the relationship between current rollingforce model output and the actual rolling force, where xaxis and y-axis represent RFa and RFma ; respectively. The upper and lower lines represent 10% deviation from the centerline. As shown in Fig. 4, large variations and positive offset values of prediction error clearly show
D. Lee, Y. Lee / Control Engineering Practice 10 (2002) 473–478
476
Data source: 990531_990630(11090 coils) in No. 1 HSM, Pohang Works 1400
1200
1200
Recalculated rollng force [ton]
Output of roll force model with actual value [ton]
Data source: 990531_990630(11090 coils) in No. 1 HSM, Pohang Works 1400
1000
800
600
400
200 200
1000
800
600
400
400
600
800
1000
1200
200 200
1400
400
600
Measured rolling force [ton]
800 1000 Measured rolling force [ton]
Fig. 6. Relation between RFa and 89:8377%; and hit rate ¼ 82:4346%:
Fig. 4. Relation between RFa and RFma :
1200
1400
RFma ð1 þ xcl ðtÞÞ: PAM ¼
Data source: 990531_990630(11090 coils) in No. 1 HSM, Pohang Works 1400
Table 1 Comparison between first and non-first coils
FSU setup rollng force [ton]
1200
1000
Order
PAM (%)
PAS (%)
Hit rate (%)
First Non-first
80.94 94.44
64.10 79.66
69.57 89.09
800
Data source: 990531_990630(11090 coils) in No. 1 HSM, Pohang Works 1400 600
non first coils of each lot first coils of each lot 1200
200 200
400
600
800 1000 Measured rolling force [ton]
Fig. 5. Relation between RFa hit rate ¼ 82:4346%:
1200
1400
and RFr : PAS ¼ 74:3553%; and
that the rolling-force model has more inherent errors in itself. However, if the correction term from short-term learning is applied to rolling-force model output, then the prediction ability is considerably improved as shown in Figs. 5 and 6. Fig. 5 shows the relation between FSU predicted rolling force RFr and measured rolling force RFa : Fig. 6 shows the relation between recalculated rolling force RFma ð1 þ xcl ðtÞÞ and measured rolling force RFa ; where hit rate means the percentage of coils of which strip thickness error falls within 750 mm: The difference between PAS and PAM comes from the external disturbances. Next, collected data are sorted into first and non-first coils in the lot, and corresponding PAM, PAS and hit rate are calculated as shown in Table 1.
Recalculated rollng force [ton]
400
1000
800
600
400
200 200
400
600
800 1000 Measured rolling force [ton]
1200
1400
Fig. 7. Comparison between first and non-first coils.
Recalculated rolling forces RFma ð1 þ xcl ðtÞÞ at first coil ( symbol) and non-first coils ( symbol) are displayed in Fig. 7: a large number of symbols move out of 10% error lines. Both Fig. 7 and Table 1 show that the first rolling coils of the lot have a lower prediction ability than that of non-first coils. These results clearly reflect that the performance of the shortterm learning is good at compensating the thickness errors from the second coils of the lot. However, the big
D. Lee, Y. Lee / Control Engineering Practice 10 (2002) 473–478
error in the first coil shows the limitation of short-term learning.
477
follows: RFr ¼ ð1 þ xnn ðtÞÞRFm : While, for the remaining coils, the rolling-force prediction is determined using the conventional short-term learning output xcl ðtÞ as follows:
3. Long-term learning with neural network and applications
RFr ¼ ð1 þ xcl ðtÞÞRFm : The limitation of conventional short-term learning lies in its use of the one-step previous xcl ðt 1Þ in Eq. (5). Within the same lot, xcl ðt 1Þ is updated so that it compensates for the newest model error after rolling. However, xcl ðt 1Þ just after lot change is not updated because rolling is not done. Then, it contains past compensation value of model error and when this is not proper for current rolling, it can lead to large rollingforce prediction error after lot change. To cope with the limitation of conventional shortterm learning, this paper suggested a long-term learning scheme using neural-network (see Fig. 8). By using the good non-linear mapping capability of neural-network, it is trained to fully learn the model error at specific input conditions. Since neural-network compensation is not directly affected by previous xcl ðt 1Þ; the accuracy of rolling-force prediction can be maintained high, irrespective of lot changes. For implementation purpose, neural-network compensation is applied at the first coil after lot change, while conventional short-term learning output is used for remaining coils of the lot. The design of neural-network is done as follows. The neural-network is trained to map the non-linear function RFa =RFma 1: After training, the prediction of rolling force is performed as follows. For the first-coil of the lot, the rolling-force prediction is done using the neural-network output xnn ðtÞ as
According to our simulation, the combination method (multiply or addition type) of the neural-network and the mathematical model does not affect the results much. From the several simulation tests, one hidden layer for the neural-network is selected and the tangential sigmoid function is used as non-linear function of neuron. The input parameters are determined by considering the mathematical model inputs and engineers’ experiences. The selected 16 inputs are as follows: xðt 1Þ; RFm ; target strip thickness, target strip width, work roll speed, temperature, C, Mn, Si, B, Mo, Ti, Nb, Cr, furnace duration time, and furnace number. Among them, C, Mn, Si, B, Mo, Ti, Nb and Cr are the chemical components. Especially, since furnace number and furnace duration time highly affect the rolling conditions in our target system, they are used as neuralnetwork input. All input variables are normalized as follows: x mx x# ¼ ; sx where x is the input variable, mx is the mean value of input variable, and sx is the standard deviation. For training, about 15,000 coils are selected and Levenberg–Marquardt back-propagation algorithm (Hagan & Menhaj, 1994) is used.
eoff =
Off-line Learning (Long Term) ξ NN NN1 (1 + ξ NN ) Σ
RFa −1 RFma
Calc. Error2
1 Rolling Conditions
MM
Π
f(...)
RFr
ξ CL CL
RFm
RFa SDr
(1 + ξ CL )
Σ
Scr ew Down Calc. e =
PLANT Calc. Error1
Actual Data
MM RFa
on RFma 1 On-line Learning (Short Term)
RFma
−1
RFr = (1 + ξ NN ) RFm (For First Coil) RFr = (1 + ξ CL ) RFm (For Non First Coil)
ξ CL (t + 1) = (1 − α )ξ CL (t ) + αeon (Short Term Learning) Fig. 8. Block diagram of neural-network application.
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D. Lee, Y. Lee / Control Engineering Practice 10 (2002) 473–478
Conventional
Proposed
Fig. 9. On-line test results at first coils.
With the neural-network long-term learning, PAM is increased by 6.2% and hit rate by 2.1% in no. 6-stand. The averaged thickness error and standard deviation decrease by 7.3 and 2:2 mm; respectively (see Fig. 9). In the case of number 5 stand, hit rate and averaged thickness errors, standard deviation improve by 3.2%, 9.4, 2:4 mm; respectively. In addition, this improvement increased the overall thickness accuracy of the strip.
4. Conclusion In this paper, a long-term learning method using neural-network is proposed to improve the accuracy of rolling-force prediction in hot-rolling mill. From the statistical analysis, it is found that severe thickness error exists in the first-coil of the lot and the conventional learning scheme is not useful to compensate the error at this point. Thus, to solve this problem, neural-network method is combined with the conventional learning algorithm in the pre-calculation stage. By doing so, considerable thickness improvements are obtained in Pohang No. 1 hot strip mill of the Republic of Korea. However, in order to adapt the neural-network properly to process variations, its training needs to be done periodically with a large number of data. Current weight update is done off-line, while the procedures such as data gathering, filtering, training, checking, etc. can
be a burden to the operator. Thus, for ease of maintenance and effectiveness, of neural-network training method, an update of its weight in online is considered as the topic of future study.
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