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NISCO Plate/Coil Mill Level 2 Force Model Improvements



2.1 Level 2 Learning Logics Issues and the Solution

In the Level 2 model, the roll separating force is continuously optimized through learning by comparing measured and predicted force values, and the learning is usually performed with flow stress. In the NISCO Level 2, the following formula is used for the flow stress modeling:


The four parameters C1, C2, C3 and C4 represent the coefficients of material, temperature (T in K), strain (φ) and strain rate (u in /s), respectively. NISCO Level 2 uses adaptive learning. The learning includes the short-term or pass-to-pass learning to shift the values upwards or downwards based on the error in the previous pass, and the long-term learning to recalculate and adjust the coefficients after a qualified piece is rolled. The long term learning of this Level 2 initially used four fitting mechanisms as showed in the left column of the Table 1 (for whatever reason, there is no FIT4 in NISCO Level 2).

Table 1: Existing and Improved Learning Logics


Learning Coefficient

Original Learning

Improved Learning


C1, C2

C3=0, C4=0

C3=C3m, C4=C4m


C1, C2, C3

C4 =0



C1, C2, C4




C1, C2, C3, C4


Hereby would several weaknesses in the existing Level 2 package be summarized, as identified in the earlier work [1].

  1. Learning Logic Issues. Initially, if a coefficient is not used for learning, its value was set as zero (the "Original Learning" in Table 1). The issue here is, that for example, if C3=0, it actually assumes the strain, or the draft, has no effect on the roll force. This is a logical problem existing in the TIPPINS level 2 model, and it leads to a much higher C4 value. Similarly, C4=0 creates a much higher C3 value. This logical error results in fluctuation in C3 and C4, as was observed in the log files. Therefore, the average coefficients, as showed in the column "Improved Learning", are preferred. The C3m and C4m can be provided through offline design, and this is the first reason such flow stress coefficients should be designed.
  2. Limitation of Adaptive Learning. There is a common limitation for the adaptive learning in this case. Level 2 data shows, in the piece-to-piece learning, it often happens that for one piece, a small C3 plus a large C4 combined achieves good prediction accuracy, while for another piece, a large C3 plus a small C4 combined works well. In contributing those C3 and C4 to the long term learning values, it will hurt the long term learning, because either C3 or C4 could be any value. This is the second reason that a designed C3 and C4, rather than those from blind learning, should be used. This limitation also causes fluctuation of flow stress coefficients and greatly hurts the accuracy of the force prediction. A blind learning without such a design for C3 and C4 would only lead to limited accuracy.
  3. Metallurgical Effects. In designing the C3 and C4, a great number of factors, primarily the metallurgical effects such as retained strain caused by incomplete recrystallization, etc., should be considered.

The influence of the above-mentioned factors on the C3 and C4 was well discussed in the earlier paper [1] for the EOS project.

2.2 The Guided Two-Parameter Fitting (FIT2G)

For the reasons discussed above, in the past projects, a simple but very effective learning procedure called Guided Two-Parameter Fitting (FIT2G), has been developed [2]. It uses carefully designed medium values for C3 and C4, and performs adaptation by adjusting C1 and C2. This procedure can, not only remove the learning logic issues and the limitation of the adaptive learning, but also include the metallurgical effects into the Level 2 model.

To increase accuracy of rolling force predictions across various products, flow stress model maintains separate sets of flow stress coefficients for each model grade. A model grade is usually created based on the steel grade (chemical composition), product (type and dimension) and production practice (e.g., regular or controlled rolling), and so on. For each model grade, there are three sets of coefficients that are automatically adjusted by the long-term learning function to cover three ranges of either thickness or temperature expected during rolling. Therefore, key steps for the FIT2G consists of: (1) designing model grade list, and (2) designing flow stress coefficients for each model grade in each temperature region.

The large number of flow stress coefficients, usually 6,000-20,000 sets of C1, C2, C3 and C4 for a plate mill, are the results of all the solutions for the learning logics, limitation of adaptive learning, and metallurgical effects. In addition, it only requires very limited modifications to the Level 2 source code and needs a very small temperature range (number of points) to perform regression. Therefore, it is the right solution for improving existing Level 2 models and for handling tough rolling condition, even the rolling in two-phase region. This procedure achieves very high force prediction accuracy, dominantly within 5% for reversing rolling of plate coil in e.g. NISCO steckle mills (for strip rolling, it is expected to achieve a force error below 1%).

The Guided Two-Parameter Fitting can be applied not only to design new but also particularly to improve existing Level 2 models. Primary advantages are summarized below.

  1. Resolves the issue that the effect of strain and/or strain rate is ignored (e.g., by using C3=0 and/or C4=0) in force prediction. Carefully designed C3 and C4 precisely consider the effects of the strain and strain rate.
  2. Removes the limitation of adaptive learning, e.g. due to dependence of C3 and C4 on each other. The model can thus continue to improve itself, and to achieve very high accuracy.
  3. Requires very few modifications to the source code, which is very suitable for improving exist Level 2. It reduces the concern of introducing new errors into the system.
  4. Considers metallurgical effects. The complicated metallurgical effects can be fully represented by a large number of well-designed flow stress coefficients. This is an elegant and effective way to integrate metallurgical principle into Level 2 system.
  5. Has very high prediction accuracy. As indicated in the paper [1], even for the hard and thin grades that had had frequent shape defects and force error up to 40%, the testing with this learning mechanism still achieved an average error of mere 3.4%.
  6. Requires as low as two passes for adaptation, and thus needs very narrow temperature range. It is possible to greatly improve finish shape by narrowing the third temperature range.
  7. Has high calculation speed. A special benefit exists in the high-speed calculation because it only needs to recalculate two coefficients C1 and C2, instead of four (C1 to C4).
  8. Minimizes project risk. The procedure turns most of work from online coding into offline design, and thus greatly reduces side effect of the system upgrade.

Learning is a great feature of the modern online system. However, if it is blind learning, or if the logic is defective, it may cause significant damage. On the other hand, pre-existing logics may fail when the system gain more complicity, such as when microstructure model is integrated into the Level 2 system. The Guided Two-Parameter Fitting has avoided all those traps in a very simple way. In designing new Level 2 model, the design logics in the FIT2G can be integrated into it to establish a hybrid solution for the neural network learning or adaptive learning.


<To Be Continued>


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