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In early March 2007, the newly designed coefficients for the four most troubled model grades (for hard and thin products), as listed in Table 4, were entered into the Level 2 system for a trial. The model grade 05010531CN1 caused a redrafting (redistribution of draft) due to poor force predictions, so for this grade the system was switched back to use the original coefficients. In this very early stage, coefficients C₁ and C₂ had not yet been fully tested against the large amount of historical data. This might have been the reason for the difference between the new and old models behavior that led to the redrafting. The idea mentioned in section 3, that C₁ and C₂ should also be carefully designed and fully tested against historical data, came from this redrafting case. The satisfactory results from the tests provided encouragement for the completion of the remaining grades, with over 6000 sets of flow stress coefficients being designed.

Table 4: Model grades for testing

For grade 05010002SN1, 13 of the 15 passes were within an error of 5%. The maximum errors with the old model were 12-14%. With the new model, the maximum errors were about 10%, which were encountered in the penultimate pass.

Fig. 2: Slab NT2254A5 of Grade 05012506CN1

The predicted values for Grade 05012506CN1 from the old and the new models were compared with the measurements, as showed in the Fig. 2. The old model led to an error over 20%. The new model showed improvements, but still, with fairly high errors slightly over 10%. The fact that the new model still had certain error in those two model grades could be explained.

• No X-Ray correction was observed that would indicate an inaccurate gage-meter from the AGC.

• It is believed that there was a phase transformation in the last pass, so the much softer ferrite was generated. In the measured data (Fig. 2), from the penultimate pass to the last pass, the flow stress went lower with decreasing temperature. Further data processing to draw the flow stress curves vs. temperature at a constant strain (0.3) and constant strain rate (10/s) showed the same trend [8]. The logical explanation is that a newer, softer material (ferrite) was generated through metallurgical transformation (in austenite). In this case the flow stress model failed because more than one materials (phases) were involved.

• The range of the third temperature region was too wide and thus there were too many passes in the region. Although passes are weighted more heavily towards the last pass, this negatively affected the learning regression.

If those two problems had not been significant, a much higher accuracy would have resulted, as in the case of the model grade 04010531CN1, showed in Fig. 3. With the new model, the errors for all passes were near or below 5%. With the old model, however, there were still 40% passes with errors beyond 5%. The better results obtained with this grade over the previous example may also be attributed to the larger final thickness of the product (grade 04010531CN1, "04" series, with its name starting with "04") than the other two grades ("05" series). It is expected that for the thick grades ("03", "02" and "01" series), most passes would enjoy a small force error below 5%, while a small portion of passes with 5-10% error.

Fig. 3: Grade 04010531CN1, Slab NT2291A4

<To Be Continued>

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