JPH11104720A - Setup equipment of rolling mill - Google Patents

Abstract

PROBLEM TO BE SOLVED: To achieve accurate and stable setting-up of a rolling mill by expressing the setup model in the form of weight sum of explanatory variables and correcting the weighting factor by sequential method of least squares. SOLUTION: A measured value collecting means 3 collects measured values of, for example, flow stress and reduction stress and the like when a rolled material 2 is cold-rolled or hot-rolled by a rolling mill 1. A sequential least square calculation means 4 calculates the weighting factor of the setup model on the basis of the measure value collected by the measured value collecting means 3. A setup calculation means 5 determines the setup values of the rolling mill 1 on the basis of the weighting factor calculated by the sequential least square calculation means 4. Also, the setup calculation means 5 determines the setup values of the rolling mill 1 of reduction amount, rolling load, and reduction position each pass time when the rolled material 2 is passed through the rolling mill 1 on the basis of respective mathematical models.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a rolling mill set-up apparatus, and more particularly, to a rolling mill set-up apparatus that corrects a setup model based on actual measurement values observed during rolling.

[0002]

2. Description of the Related Art In a rolling process, it is possible to achieve a desired finished shape and finished size while minimizing the total rolling time under various constraints on a rolling mill, such as a motor torque, a rolling load, and a rolling reduction. Desired. For this reason, a setup value (set value) of the rolling mill, such as a roll gap and a roll speed, must be appropriately determined for each pass of the rolled material passing through the rolling mill. Usually, this setup value is calculated by a mathematical model (setup model) based on rolling theory. For example, the setup model used in calculating the rolling load is a rolling load model itself, a temperature model, a rolling torque model, and the like. However, even if the characteristics of the rolling mill are the same, the characteristics of the rolling mill are slightly different from each other, and may change over time. Therefore, in order to improve the setup accuracy, it is essential to appropriately modify the setup model based on the actually measured values actually observed. A setup apparatus for a rolling mill that appropriately corrects a setup model based on actual measurement values as described above is disclosed in, for example, Japanese Patent Application Laid-Open No. 50-108150 (hereinafter, referred to as Reference Document 1). In apparatus as described in the reference document 1, on the basis of the correction factor Z as shown below, for example, the calculated value F _c of the rolling load is corrected, rolling load prediction value F to be applied to the next set-up is required . Here, the correction factor Z is, Z = F _A / F _c where, F _A; a measured value of the rolling load, rolling load prediction value F to be applied to set up
Is F = _Fc · Z ′, where Z ′ is a correction coefficient for the next time. In particular, in this apparatus, the next-time correction coefficient Z 'is statistically learned based on the difference between the current correction coefficient Z and the average value m of the past correction coefficients, thereby improving the setup accuracy. Further, in the apparatus described in Japanese Patent Application Laid-Open No. 1-133606 (hereinafter referred to as Reference Document 2), not only the correction coefficient Z ′ concerning the calculated value, but also a factor (for example, a reduction ratio) which affects the calculated value, explanatory variable) performs coefficient a _n all learning according to X _n. That is, rolling load prediction value F _{is, F = F c · Z '} · Qs _{However, Qs = a 0 + a 1} X 1 + a 2 X 2 + ... + a n X n a n; determined by the explanatory variable; weighting coefficient X _n is, learning proceeds performed manually or automatically regression calculated for the weighting factor a _n.

[0003]

However, as in the prior art described in the above-mentioned reference 1, when the correction coefficient Z relating to the calculated value is learned to improve the setup accuracy, the setup model is used for the learning. Because the physical meaning is not taken into account, the cause of the error cannot be identified,
The effect of adaptive control is small. Further, when the learning of the correction function Qs is advanced by multiple regression calculation as in the prior art described in the above-mentioned reference 2, the inverse matrix for performing the regression calculation may not be obtained based on the actually measured data to be learned. Can not do. Further, since regression calculation cannot be performed until data has been accumulated to some extent, it is not possible to make the correction of the coefficient quickly follow the characteristic variation of the process. In order to solve the problems in the conventional technology, the present invention improves a rolling mill set-up device, expresses a set-up model in the form of a weighted sum of explanatory variables, and modifies weighting factors by a sequential least squares method. By doing
It is an object of the present invention to provide a rolling mill set-up device capable of setting up a rolling mill with high accuracy and stability.

[0004]

SUMMARY OF THE INVENTION In order to achieve the above object, the present invention provides a rolling mill set-up apparatus for setting up a rolling mill based on a calculated value calculated from a model formula. , And is configured as a rolling mill set-up device characterized by modifying the above model formula by a sequential least squares method. In the setup device of the rolling mill, the above model formula is corrected by the sequential least squares method, so there is no need to calculate the inverse matrix or store some data as in the case of performing multiple regression calculation. , It is possible to automatically perform a stable setup.
In addition, since the model formulas are sequentially modified by the sequential least squares method, it is possible to quickly respond to process characteristic fluctuations. Further, the modeling error is absorbed for each explanatory variable, so that the setup accuracy can be improved.
In the set-up device of the rolling mill, for example, a model expression relating to the deformation resistance of a rolled material is used. Further, regarding the deformation resistance having a low model accuracy, for example, by using the model equation shown in equation (A),
The weighting coefficient of the equation (A) can be corrected for each pass by the sequential least squares method, and accurate setup can be performed. K _f = a ₀ + a ₁ / T + a ₂ ε + a ₃ Ａ (A) where K _f ; deformation resistance, T; absolute temperature, ε;
ζ; strain rate a ₀ , a ₁ , a ₂ , a ₃ ; weighting coefficient. Further, with respect to the deformation resistance, it is also possible to correct the weighting coefficient of the equation (B) for each path by using the model shown in the equation (B) sequentially by the least-squares method, thereby performing an accurate setup. . log (K _f ) = a ₀ + a ₁ / T + a ₂ log (ε) + a ₃ log (h) (B) where K _f : deformation resistance, T: absolute temperature, ε: rolling strain,
h: delivery side plate thickness a ₀ , a ₁ , a ₂ , a ₃ ; weighting coefficient. Further, by using the model equation relating to the error between the calculated value of the rolled material and the actual value, it is possible to set up the rolling load with high accuracy.
For example, as the model formula relating to the error, a model formula shown in formulas (C) and (D) is used. _{ΔP = a 0 + a 1 K} f + a 2 μ (C) ΔP = a 0 + a 1 K f + a 2 μ + a 3 T (D) wherein, [Delta] P; load prediction error, K _f; deformation resistance, mu; coefficient of friction, T; absolute temperature _{a 0, a 1, a 2} , a 3; is a weighting factor.

[0005]

Embodiments of the present invention will be described below with reference to the accompanying drawings to provide an understanding of the present invention.
The following embodiment is a specific example of the present invention and does not limit the technical scope of the present invention. Here, FIG. 1 is a diagram showing a schematic configuration of a setup device of a rolling mill according to an embodiment of the present invention, and FIG. 2 is a diagram showing a procedure for determining a setup value by setup calculation means. As shown in FIG. 1, a rolling mill set-up apparatus 0 according to an embodiment of the present invention performs, for example, deformation resistance, rolling distortion, etc. during cold or hot rolling in which a rolling material 2 is rolled by a rolling mill 1. An actual measurement value collecting means 3 for collecting actual measurement values, a sequential least square operation means 4 for sequentially performing a least square operation on the weighting coefficient of the setup model based on the actual measurement values collected by the actual value collection means 4, A setup calculation means for determining a setup value of the rolling mill based on the weighting coefficient calculated by the least square calculation means. As shown in FIG. 2, the setup calculation means 5 sets up the setup values of the rolling mill 1 such as the reduction amount, the rolling load, the reduction position, etc., in accordance with each mathematical expression for each pass through which the rolling material 2 passes through the rolling mill 1. Determined based on the model. Among these setup values, the rolling load model has the greatest influence on the setup accuracy. Here, the following equation (1) shows an example of a rolling load model. _{P = B · Q p · I} d · K f (1) However, P; rolling load, B; strip width, Q _p; rolling force function,
I _d ; contact arc length, K _f ; deformation resistance Among these rolling load models, the deformation resistance K _f is particularly difficult to model, and its error is large.

Therefore, in the following, for the sake of concreteness, the weighting coefficient is sequentially determined by the least squares calculating means 4 for the deformed resistance model expressed in the form of a weighted sum, and the setup calculating means 5
The calculation of the setup value of the rolling load P will be described below. The deformation resistance K _f included in the rolling load models, empirically absolute temperature T, pressure strain epsilon, are known to depend often strain rate zeta. The sequential At least square calculation means 4, representing the deformation resistance K _f in the form of a weighted sum, such as the following equation (2) or (3), the recursive least square method to setup calculation means 5 defining a weighting factor Output. K _f = a ₀ + a ₁ / T + a ₂ ε + a ₃ ζ (2) where K _f : deformation resistance, T: absolute temperature, ε: rolling strain,
ζ; strain rate a ₀ , a ₁ , a ₂ , a ₃ ; weighting coefficient. Also, θ ^T = (a ₀ , a ₁ , a ₂ , a ₃ ), ψ ^T =
If (1, 1 / T, ε, ζ), the above equation (2) is expressed as K _f = ψ ^T θ (3). Here, FIG. 3 shows a procedure for calculating the rolling load P by the setup calculating means 5, and FIG. 4 shows a procedure for determining the weighting factor by the sequential least squares calculating means 4. FIG.
As shown in, the setup operation means 5, flattened roll radius (contact arc length I _d) calculating, plate width B read, rolling force function Q _p calculation or the like, the rolling load P is calculated according to the equation (1). For model less accurate deformation resistance K _f is the weighting factor read from recursive least square operation unit 4 in the calculation is used. The calculation of the weighting coefficient by the sequential least squares calculating means 4 is performed according to the procedure shown in FIG. That is,
The measured values of the deformation resistance K _f , temperature T, rolling strain ε, and strain rate の of the previous pass collected by the measured value collecting means 3 are read, and the consistency of each variable is checked. The weight coefficient θ is updated. Details of updating the weight coefficient θ will be described below.

In the deformation resistance model such as the above equation (2) or (3), if the deformation resistance K _f , the absolute temperature T, the rolling strain ε, and the strain rate あ る, which are input / output variables, are measured for each pass. For example, a simultaneous equation (2a) or (3a) relating to i number of weighting factors can be obtained in the path i with the equation error as r. _{K f (1) = a 0} + a 1 / T (1) + a 2 ε (1) + a 3 ζ (1) + r (1) · · · · (2a) K f (i) = a 0 + a 1 / T (i) + a ₂ ε (i) + a ₃ ζ (i) + r (i) or K _f (1) = ψ ^T (1) θ + r (1) (3a) K _f (i) = ψ ^T (i) θ + r (i) That is, for the above simultaneous equations (2a) or (3a), the weighting coefficient θ that minimizes the sum of squares of the equation error r (i) is obtained, whereby the deformation resistance model can be identified. It becomes possible. Here, for example, the sum of squares (evaluation function) J of the equation error r (i) in the simultaneous equation (3a) is expressed by equation (4).

(Equation 1) Further, the weight coefficient θ that minimizes the evaluation function J is obtained by Expression (5).

(Equation 2) Meanwhile, it sets the weight coefficient theta from the above equation (5), although variations are possible for calculating the resistance K _f, must be performed to calculate the inverse matrix in order to determine the weighting coefficients theta, multiple regression calculation Therefore, it is necessary to store the actually measured value data through a certain number of passes i.

In the setup device 0 of the rolling mill, the weighting coefficient θ is not determined by using the above equation (5), and the weighting coefficient θ is sequentially corrected by performing a sequential calculation. That is, the sequential least squares method is used. For example, in the above equation (5),

(Equation 3) Then, the above equation (5) can be transformed into an equation (7).

(Equation 4) Equation (6) is

(Equation 5) By substituting equation (8) into equation (7), the following recurrence equation, that is, a sequential calculation algorithm can be obtained.

(Equation 6) Further, the recurrence formula (9) can be summarized as a formula (10) that does not calculate the inverse matrix.

(Equation 7) If the forgetting factor γ is introduced into the recurrence equation (10),

(Equation 8) It is expressed as The value of this forgetting coefficient γ is, for example, the path i
Is a coefficient approaching 1 with the passage of time, and the weighting coefficient θ
This is to reduce the contribution of the old path in making the determination, that is, to make it forget. By introducing the forgetting factor γ,
It is possible to cope with relatively slow fluctuations. According to the recurrence formula (10) or (11) as described above, the new weight coefficient θ (i) is obtained by comparing the immediately preceding value θ (i−1) with the measured deformation resistance values K _f (i) and ψ The weight coefficient θ can be obtained from (i-1), and there is no need to calculate the inverse matrix. Therefore, stable learning (parameter update) with good responsiveness can be performed.

[0009] When the sequential least squares calculation is performed, initial values of θ, K, and D are required in the first pass after the calculation, and these values are stored in the past data (for example, 1).
The final θ, K, D (the result of the 100th pass) obtained by applying the sequential least squares method offline to the (data of the 00th pass) are used. Of course, in subsequent passes, θ, K, and D obtained in the previous pass are sequentially used. FIG. 5 shows the result of learning the deformation resistance model in this way and obtaining the rolling load using the learning result. The horizontal axis in FIG. 5 is the number of rolling passes, the vertical axis is the ratio between the predicted value and the actually measured value, and the white circle shows the result of the present invention and the black circle shows the result of the conventional apparatus. As shown in FIG.
Although the conventional apparatus cannot absorb the fluctuation of the process characteristics caused by the number of rolling passes about 50 times, the measured value / calculated value fluctuates between 1.1 and 1.2 after the fluctuation. At 0, the number of rolling passes is about 105, and the influence of the characteristic fluctuation is substantially absorbed, and thereafter, high-precision control in which the measured value / calculated value is close to 1 is performed. As described above, in the rolling mill set-up apparatus according to the present embodiment, the deformation resistance model is expressed in the form of a weighted sum, and the weighting factor is updated for each pass by the sequential least squares method, thereby achieving a stable and accurate setup. Can be performed.

[0010]

[Embodiment] In the above embodiment, a deformation resistance model as shown in equation (2) is used. However, another deformation resistance model as shown in equation (12) expressed in the form of weighted sum is used. Is also good. That is, it is possible to select a model that is considered to be the most reliable for the rolling mill to be applied.

(Equation 9) Further, another deformation resistance model represented by the following equation (13) using the exit side plate thickness of the rolled material 2 may be used. log (K _f ) = a ₀ + a ₁ / T + a ₂ log (ε) + a ₃ log (h) (13) where K _f : deformation resistance, T: absolute temperature, ε: rolling strain,
h; Discharge side sheet thickness In addition to the deformation resistance model, the rolling force function and the rolling load model included in the rolling load model are expressed by, for example, the formula (1).
4) and (15), each of which may be expressed in the form of a weighted sum, and the weighting coefficient may be sequentially updated by a sequential least squares method. That is, the present invention can be applied not only to the deformation resistance model but also to a model with low accuracy to improve the setup accuracy of the rolling mill.

(Equation 10)

[Equation 11] Of course, for other torque functions and the like, for example, Equation (1)
It is possible to express the weight sum as in 6) and perform adaptive control.

(Equation 12) Further, the sequential calculation algorithm used in the sequential least squares calculating means 4 is also expressed by Expression (10) and Expression (1).
However, the present invention is not limited to 1). For example, a sequential calculation algorithm such as Expression (17) using a square root filter may be used to guarantee the positive definiteness of the D matrix. Such a rolling mill setup device is also an example of the rolling mill setup device in the present invention.

(Equation 13)

In the above-described embodiment, the weight sum is used.
The weight coefficient of the model formula itself such as the expressed deformation resistance is sequentially calculated.
Corrected by the least squares calculation means 4, for example,
Model on the Error between the Calculated Value of Rolling Load of Steel and the Actual Value
The (error model) equation is successively calculated by the least squares calculating means 4.
The weighting factor is corrected, and the model
Add the calculated error to the calculated value of the model formula itself
Thus, the calculated value may be corrected. here
FIG. 6 shows the procedure for calculating the rolling load using the above error model.
FIG. 7 shows a procedure for updating the weight coefficient of the error model. Figure
As shown in Fig. 6, when calculating the calculated rolling load,
Flat roll radius (contact arc length I_d), Rolling force function Q_p, Strange
Shape resistor K_fIs calculated. In this example, the deformation resistor
Anti-K_fIs not updated. Next, plate width B
Is read, and the error model for the rolling load P is calculated.
Calculation is performed. For example, the above model relating to the load P of the rolled material
For equation (1), the actual measured value is P_rWhen
Then, the error ΔP = P-P_rThe following equation (1
The error model can be expressed by 8) or equation (19).
You. ΔP = a₀+ A₁K_f+ A_Twoμ (18) ΔP = a₀+ A₁K_f+ A_Twoμ + a_ThreeT (19) where μ: coefficient of friction, a₀, A₁, A_Two, A_Three;weight
Coefficient In the above error model, the friction coefficient that has a particularly strong correlation with the error ΔP
Several μ and deformation resistance K _fUse absolute temperature.
However, it is not limited to this. And above
It is not about the model equation (1) itself, but the above error model.
Weighting coefficient θ (a) for equations (18) and (19)₀, A
₁,...) Are updated according to the procedure shown in FIG.
As shown in Fig. 7, the error model value of the previous pass is calculated first.
And the deformation resistance K of the previous pass_fOf friction coefficient μ
The calculated value is read. Deformation resistance K of these previous passes_f,
When the consistency is confirmed for the friction coefficient μ,
Is read, and the matrices K and D are read,
The order is determined according to the above equation (10), (11), or (17).
The next operation is performed, and the new weight coefficient θ for the error model
Is calculated and updated. Then, the updated error model
Error model value Δ based on a new weighting factor θ
P is determined, added to the rolling load model P, and
Calculation of rolling load is performed. Changed process characteristics
Later, the setup value is calculated based on the error model as described above.
FIG. 8 shows the ratio between the actually measured value and the calculated value when is defined. Figure
As shown in FIG. 8, the setup of the rolling mill according to the present embodiment
According to the device, the variation is greatly reduced compared to the conventional device.
Have been. Such a rolling mill set-up device
It is an example of a setup device of a rolling mill in the present invention.

[0012]

As described above, in the rolling mill set-up apparatus according to the present invention, since the model formula used for the setup is modified by the sequential least squares method, the inverse matrix is calculated as in the case of performing multiple regression calculation. It is not necessary to perform the operation or accumulate data to some extent, and it is possible to automatically perform a stable setup. In addition, since the model formulas are sequentially modified by the sequential least squares method, it is possible to quickly respond to process characteristic fluctuations. Further, the modeling error is absorbed for each explanatory variable, so that the setup accuracy can be improved. Therefore, it is possible to perform an accurate setup for a rolling load or a deformation resistance having a low model accuracy, for example.

[Brief description of the drawings]

FIG. 1 is a diagram showing a schematic configuration of a rolling mill set-up device 0 according to an embodiment of the present invention.

FIG. 2 is a diagram showing a procedure for determining a setup value by a setup calculation unit.

FIG. 3 is a diagram showing a procedure of rolling load calculation by a setup calculating means.

FIG. 4 is a diagram showing a procedure for updating a weighting coefficient by a sequential least squares calculating means;

FIG. 5 is a diagram for explaining the setup accuracy of the rolling mill set-up device 0.

FIG. 6 is a diagram showing a procedure of a rolling load calculation in a rolling mill set-up device according to an embodiment of the present invention.

FIG. 7 is a diagram showing a procedure of updating a weight coefficient in the setup device of the rolling mill according to the embodiment of the present invention.

FIG. 8 is a view for explaining the setup accuracy of the rolling mill set-up device according to one embodiment of the present invention.

[Explanation of Signs] 1 ... Rolling mill 2 ... Rolled material 3 ... Measured value collecting means 4 ... Sequential least square calculation means 5 ... Setup calculation means

 ──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Sadao Morimoto 1 Kanazawacho, Kakogawa City, Hyogo Prefecture Inside the Kobe Steel Works Kakogawa Works (72) Inventor Hiroshi Narazaki 1-5-5 Takatsudai, Nishi-ku, Kobe City, Hyogo Prefecture No.Kobe Steel, Ltd.Kobe Research Institute

Claims (7)

[Claims] 1. A rolling mill set-up device for setting up a rolling mill based on a calculated value calculated from a model formula, wherein the model formula is expressed in the form of a weighted sum of explanatory variables, and the above-mentioned model formula is represented by a sequential least squares method. A rolling mill set-up device characterized by modifying a model formula. 2. The rolling mill set-up apparatus according to claim 1, wherein said model formula relates to a deformation resistance of a rolled material. 3. A model equation relating to the deformation resistance is (A)
3. The rolling mill set-up device according to claim 2, wherein the weighting factor of the formula (A) is corrected for each pass by a sequential least squares method. K _f = a ₀ + a ₁ / T + a ₂ ε + a ₃ Ａ (A) where K _f ; deformation resistance, T; absolute temperature, ε;
ζ; strain rate a ₀ , a ₁ , a ₂ , a ₃ ; weighting coefficient. 4. A model formula relating to the deformation resistance is (B)
3. The rolling mill set-up device according to claim 2, wherein the weighting factor of the formula (B) is corrected for each pass by a sequential least squares method. log (K _f ) = a ₀ + a ₁ / T + a ₂ log (ε) + a ₃ log (h) (B) where K _f : deformation resistance, T: absolute temperature, ε: rolling strain,
h: delivery side plate thickness a ₀ , a ₁ , a ₂ , a ₃ ; weighting coefficient. 5. The rolling mill set-up device according to claim 1, wherein the model formula relates to an error between a calculated load value of the rolled material and an actual value. 6. The rolling mill set-up device according to claim 5, wherein the model formula relating to the error is shown in formula (C), and the weighting factor of formula (C) is corrected for each pass by a sequential least squares method. ΔP = a ₀ + a ₁ K _f + a ₂ μ (C) Here, ΔP: load prediction error, K _f : deformation resistance, μ: friction coefficient a ₀ , a ₁ , a ₂ , a ₃ ; weighting coefficient. 7. The rolling mill set-up apparatus according to claim 5, wherein the model formula relating to the error is shown in formula (D), and the weighting factor of formula (D) is corrected for each pass by a sequential least squares method. ΔP = a ₀ + a ₁ K _f + a ₂ μ + a ₃ T (D) where ΔP: load prediction error, K _f : deformation resistance, μ: friction coefficient, T: absolute temperature a ₀ , a ₁ , a ₂ , a ₃ ; weighting factor.