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Modeling Issues in Level 2

Please refer to Mill Level 2 Model Basics for the symbols and basic terms used in the section.

Limitation of the Adaptive Learning

A project was completed to examine a mill Level 2 model for the reason of the large force prediction errors, with the learning fits showed in the Table 1. It was detected that there was a fluctuation of the flow stress coefficients (C3 and C4) in a large range. This fluctuation of the flow stress coefficients was identified to be due to a design logic problem of the model in the use of C3 and C4 in the FIT3A and FIT3B. Studies also indicated that C3 and C4 from FIT3A and FIT3B were much larger than those from four-parameter learning. Continued studies also showed that either a low C3 plus a high C4, or a high C3 plus a low C4, would work well, in addition to a medium C3 plus a medium C4. In further studies, it was found that C3 and C4 from learning had great dependence on each other. Level 2 log data confirmed the higher values of C3 and C4 received from FIT3A and FIT3B, respectively, than the rest fits.

Even with a four-parameter learning, the (C3, C4) value pair received from a qualified piece still can be at any point in a line, and so, both C3 and C4 can be in a wide range, from negative value, zero to a value twice as high as the best value. Therefore, there is limitation for the blind learning, simply because C3 and C4 depend on each other. It is very hard to achieve the best value by combining those widely scattered numbers. This means that the learning itself can only reach a certain level of accuracy, but no further improvement. Human intervention or other improved logic is needed to achieve high-quality learning.

An Effective Solution for Existing Level 2: the Guided Two-Parameter Learning (GFIT2)

Due to the dependence of the C3 and C4, the blind adaptive learning to let system calculated C3 and C4 based on the measured force is not recommended. In designing new Level 2 system, this dependence of C3 and C4 can be integrated into the learning logics to improve the long term learning. However, for an existing Level 2, in order not to make too many changes to the source code, use of carefully designed stable values for C3 and C4 is preferred and it is sufficiently accurate, say, with a force error below 5% as indicated in the results of a past mill project (Table 5) for steel plate reversing mill. For strip mill the expected force error should be much lower than 5%. On the bottom line, it is much better than the blind learning (including the four-parameter learning). Further learning will be conducted only through C1 (material coefficient) and C2 (temperature coefficient), the two primary contributors for the flow stress. This learning procedure can be called the Guided Two-Parameter Learning (GFIT2).

Table 5: Force error and quality level based on GFIT2

Before improvement

After 1st improvement

- 57% passes: < 5%
- 87% passes: < 10%
- 94% passes: < 15%
- model failed for some grades (40% force error, bad shape)

- over 80% passes: < 5%
- over 90% passes: < 10%
- over 99% passes: < 15%
- No occurrence of quality problem found yet since use of new model

* The data here were based on the troubled grades. Regular grades may have still better results

The result showed in the Table 5 was actually after the first of the two improvements for an existing Level 2 model for a reversing mill with steckle furnace to roll steel plates. The first improvement was primarily to solve the learning logical problems including:

  • System learning: applied the guided two-parameter learning

  • Metallurgical interaction: considered effects of retained strain, etc.

The second improvement, which was on the formula valid range and for the resume pass after hold, further improved the model quality.

Besides accuracy, the great benefit for GFIT2 solution exists in the high-speed calculation because it only needs to recalculate two parameters C1 and C2, instead of four (C1 to C4). The fast calculation also provides a perfect opportunity for web-based Level 2 system that Metal Pass is developing. In addition, GFIT2 makes it possible to minimize the number of passes in the third temperature region, to increase force prediction accuracy and finish product geometry.

To perform the GFIT2 learning, a great number of the carefully designed flow stress coefficients (C1, C2, C3 and C4) are needed. For the mill with the results showed in the Table 5, over 2000 model grades are rolled. For each model grade, there are three sets of the coefficients designed for the three temperature regions.

Coefficients C1 and C2 were supplied besides C3 and C4; this was to satisfy the rolling for the first piece right after the new coefficients are loaded into the Level 2 system.

Other researchers also identified the weakness of the blind adaptive learning. For example, some Japanese researchers also suggested the use C1 and C2 to perform learning while C4 and C4 were kept unchanged. However, they used only 1 set of the C3 and C4 for the learning. One of the advantages of Metal Pass solution is that we provide over 6,000 sets of the C3 and C4, instead of only one! The 6,000 sets of the flow stress coefficients (C1, C2, C3 and C4) from Metal Pass are available for the consulting.

Flow Stress Valid Range

The equation (1) is one of the oldest flow stress formula and has very limited coverage for the nature of flow stress. One typical problem for the small valid range exists in that, during the finish pass, the small strain is often beyond the valid range of this equation and relatively large force error may lead to a poor draft schedule and bad finish shape.  Modern forming process has called for comprehensive formulas for flow stress. There are various ways in expanding the equation (1) to satisfy different requirements.

However, big formulas may not necessarily do better job because on one hand it requires much higher technical understanding to handle the issues such as the mean flow stress, and on the other hand the dependence of the learning parameters (such as C3 and C4 mentioned above, and others if the formula is expended) may make the learning process worse if it is not handled correctly.

Flow stress modeling for the rolling in the two-phase region is still a difficult problem. Because different materials are involved, theoretically the entire set of the coefficients, C1, C2, C3, C4, and so on, should be different.

A modeling problem remaining unsolved in the metal forming (including steel rolling) community is to model the flow stress for the high-speed deformation with the strain rate over 500/s. It is still difficult to measure flow stress at a high strain rate. Hammering a sample can easily reach the strain rate 8000/s, but it is difficult to maintain a constant strain rate and so, the result is questionable.

Roll Gap

In nature, the roll separating force is only affected by flow stress and roll gap. Even the flow stress itself is tightly linked to the roll gap, through draft, etc.

While in the shape rolling (wire rod rolling, section rolling, etc.) the spread is an important factor, in the flat rolling, the roll deformation is truly critical for the flatness of the rolled product. Table 6 summaries roll deformation and roll related issues.

Table 6: Mechanical Factors of Roll Gap



Modeling Note

Roll Diameter

Ratio of the work and backup diameters, forward slip



Draft in the last two passes: not too big (for shape), but not too small either (for mechanical property)


Roll Flattening

Increases contact area. Needed for hot flat rolling model; critical for cold rolling

Formulas initially for cold rolling need to be fully expanded to fit hot rolling.

Roll Crown

Mechanical crown, thermal crown, roll wear, roll bending, etc. May cause difference in draft between center and side

Empirical + FEM

Roll Deflection

May cause difference in draft between center and side

Elastic FEM model preferred

Stand Deflection

May cause variation in roll gap

Empirical + FEM


Critical for cold rolling and high-speed rolling

Depending on lubricant, temperature, roll gap, speed, contact material pair, etc.

Heat Transfer

Steel/Roll, Roll cooling, Roll Lubrication, etc.

Coefficient depends on scale formation, pressure, cooling and lubrication, etc.

Clear understanding on the roll gap geometry and the mechanical, thermal and metallurgical phenomena in the roll gap is necessary to develop an accurate, yet concise Level 2 models. Knowledge on local deformation is very useful for understanding and solving the mill problems. For example, if the difference of the deformation between the middle and the side of the strip is over a certain limit, very likely there is center buckle or side wave. Studies on local draft, local spread, local elongation and local temperature, etc. were performed in Benjamin Li's Ph.D. dissertation. A simplified FEM model that only needs about 5% of the regular model may be capable of determining cross-sectional distribution of the local parameters and thus useful for Level 2 model.

Temperature-Dependent Properties

Temperature related parameters are among the most critical factors in the steel hot mill Level 2 model. Almost all the mechanical or physical properties used in the Level 2 models are strongly temperature dependent. Examples of the properties are specific heat, thermal expansion coefficient (or density), E-modulus, and Poisson ratio, etc. Using of fixed values in the model calculation introduces prediction error. An example for the collection of the temperature-dependent properties for various steel grades is www.metalpass.com/hit.

Intelligent Learning

The limitation for the adaptive learning discussed above opens the door for the intelligent learning techniques such as neural network, though for existing Level 2 system, the Guided Two-Parameter learning is much easier to implement.

Here is an example to apply an intelligent learning. Many Level 2 systems use reference table to predict steel width change. With a varied environment, the table content and table length may need to be changed through learning, but many systems have difficulty to achieve it. In this aspect, a neural network can be designed as a table-like system to update the table content and table length dynamically, based on a long list of factors such as production condition, fuzzy logic rules and contents in the expert system. The learning system can be designed so flexible that a simple change in the database of the expert system can modify the entire learning logics and learning behavior.

Intelligent learning techniques can greatly improve the accuracy of some models with high complexity, such as the microstructure model, the microstructure-integrated flow stress model and the model of rolled steel properties. The learning should be based on the rolling process models, in which the neural network provides the correcting factors for the model coefficients. Fuzzy logic rules and expert system can provide guidelines (upper and lower boundaries) for the learning. A hybrid intelligent learning system can be designed with the combination of mathematical models and the intelligent learning system.


A common way to perform roll force learning is through flow stress. Usually after each qualified piece is rolled, flow stress learning factors C1, C2, C3 and C4, denoting the coefficient of material, temperature, strain and strain rate, respectively, are recalculated. However, some Level 2 models failed to provide guideline for the learning factors, sometimes even with logical error that causes fluctuation of the coefficients (C3 or C4). On the other hand, coefficients, such as C3 and C4, are interactively affected. So for the same model grade, one pass could have C3=1.2 and C4=0.02 while another pass has C3=0.02 and C4=1.0, for example, and both passes may have good force prediction. However, in combining this two learning results, a poor model may be produced. Therefore, this kind of blind learning can only lead to limited model accuracy. Technical guidelines should be a great help for better learning and thus the higher force accuracy.

The factor φn (φ is the strain and n is the strain coefficient), when describing strain effect on the flow stress, has a narrow valid range and needs a modification for the passes with a low draft (e.g. below 10%, often in finishing pass) or a high draft.

Besides the flow stress, the force error is also likely from factors such as models of shape factor, roll flattening, roll deflection, roll crown and stock temperature, etc. In recent years, the popularity of continuous casting and rolling of flat product led to a period of intensive study of flat rolling process. The results are ready to be integrated into a quality Level 2 model. In addition, Metal Pass has developed over one hundred rolling process models based on extensive rolling tests worldwide, particularly in Germany and USA. Those models would be very helpful for improving Level 2 model accuracy.

While the traditional learning process has some weaknesses, especially in handling metallurgical issues in the Level 2 model, the intelligent learning technology under integration of neural network, fuzzy logic, and expert system, etc., can right fit the gap. The increasing computer speed makes it practical to apply the advanced learning techniques. One great application opportunity of the neural network can be the prediction of microstructure and rolled steel properties, where the final results (mechanical properties) are relatively easy to measure, but the intermediate data (microstructural parameters) for the model is extremely expensive to obtain.

Metal Pass Consulting

Level 2 Development Issues

Level 2 Model as a Metallurgical System


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