JP4047875B2 - Method for determining optimum values of design parameters and method for determining rolling pass schedule using this method - Google Patents

Description

  The present invention relates to an optimum value determining method for determining an optimum value of a design parameter in a design object having a design parameter, and a rolling pass schedule using such a determination method for designing a pass schedule in a rolling process. It relates to the decision method.

Conventionally, a number of methods have been proposed as an optimum value determination method for determining an optimum value of a design parameter in a design object having the design parameter.
One of these is the “optimization problem with constraints” as described in Non-Patent Document 1. A minimum problem with constraints refers to a design object, sets an evaluation function (objective function) including design parameters and output amounts for the design object, and minimizes the evaluation function under the constraint conditions Design parameters are determined.
The second is “optimization problem assuming probability distribution” described in Non-Patent Document 2 and Non-Patent Document 3. This technique uses the Monte Carlo method, which is a method of handling random numbers, assumes a variable distribution, and performs optimization in consideration of the probability using random numbers. Such a technique is also disclosed in Non-Patent Document 4. The technique of Non-Patent Document 4 is called FORM (First Order Reliability Method), which converts a group of random variables into uncorrelated standard Gaussian distribution variables, and the surface and coordinate origin of the limit state criterion function. The reliability index that is the minimum distance between and is searched. This method also performs an optimization calculation assuming a distribution of variables.

The above-mentioned “optimization problem with constraints” and “optimization problem assuming a probability distribution” are also disclosed in Non-Patent Document 5. That is, Expressions (10) and (11) of Non-Patent Document 5 are the constraint conditions when solving the optimization problem with the constraint conditions, and Expressions (3), (17), and (18) are the probability distributions. This is a constraint condition in an optimization problem assuming that
On the other hand, Non-Patent Document 6 is known as an application of the optimization problem to the determination of the pass schedule in the rolling process. In this technique, an evaluation function and constraint conditions are set and dynamic programming is used to determine (design) a pass schedule of a tandem rolling mill. In particular, when the rolled material is rolled from the original plate thickness (plate thickness before rolling) to the finished plate thickness, the exit side plate thickness of the rolling stand other than the final stand is optimized.
Optimal theory and optimization of systems, Hideaki Kano, Corona, 1987 Descriptive Sampling: A Better Approach to Monte Carlo Simulation, EDUARDO SALIBY, Journal of the Operational Research Society, Vol.41, No.12, pp.1133-1142, 1990 Descriptive sampling in structural safety, Kalman Ziha, Structural Safety, Vol.17, pp.33-41, 1995 STRUCTURAL RELIABILITY UNDER COMBINED RANDOM LOAD SEQUENCES, RUDIGER RACKWITZ and BERND FIESSLER, Computers & Structures, Vol.9, pp.489-494, 1978 Structural Optimization Using Probabilistic Constraints., Thanedar, PB and S. Kodiyalam, Proceedings of AIAA / ASME / ACE / AHS / ASC Structures, Structural Dynamics and Materials Conference, pp.205-212, 1991 Pass schedule optimization theory and evaluation function of rolling work, Katsura Okado, Hiroshi Suzuki, Plasticity and processing, Vol.10, no.106, 1969

The solution of the “optimization problem with constraints” has been clarified in many textbooks. However, this method usually performs optimization using one piece of data (input amount of design object, design parameter, output amount), so it is a good design for one piece of data used for the design. When the number of data is large and there are variations in data, there is a problem that there is no guarantee that the design is good.
The “optimization problem assuming a probability distribution” method allows the design considering the above-mentioned variation, but the assumption of the probability distribution has a peak such as a normal distribution or a Weibull distribution that can be converted into a normal distribution. One is usually smooth. However, in reality, the constraint condition may be a discontinuous distribution having two or more peaks. If such a distribution is forcibly applied to a conventional method and approximated by a normal distribution or the like, the optimum value of the design parameter cannot be obtained accurately. Furthermore, it is often difficult to determine a probability distribution when the number of data is small.

On the other hand, suppose that the above-mentioned “optimization problem with constraints” and “optimization problem assuming a probability distribution function” are applied to determine the rolling pass schedule in the rolling process.
In the rolling process, a rolled material having a predetermined plate thickness is rolled to a target finished plate thickness on the exit side of the final stand. At this time, there is a degree of freedom in setting the thickness of the stand exit side other than the final stand or the tension between the stands.
For example, in a tandem type rolling mill having five rolling stands, it is possible to reduce the plate thickness evenly from # 1 stand to # 5 stand, and to greatly reduce the plate thickness relatively upstream. Is also possible. Such setting of the plate thickness is called a rolling pass schedule or simply a pass schedule.

In addition, although a pass schedule normally refers to the delivery side plate | board thickness in rolling stands other than a final rolling stand, the case where it is the tension | tensile_strength between stands and the case where it is both the said delivery side plate | board thickness and the tension | tensile_strength between stands shall be included. This is because there is no difference between the exit side plate thickness and the inter-stand tension in that it is a variable that affects the rolling state, and the target value is determined before rolling in both cases.
For example, in the case of a rolling mill having five rolling stands, the pass schedule is the thickness of the exit side of # 1 rolling stand to # 4 rolling stand and / or # 12, # 23, # 34, # 45 stand. Intertension will be shown. For example, “tension between # 12 stands” means tension of # 1 rolling stand to # 2 rolling stand.

Further, in the rolling mill, when the entry side tension and the exit side tension can be set, the entry side tension and the exit side tension of the rolling mill can be included in the inter-stand tension adopted as the pass schedule.
In a conventional method for determining a rolling pass schedule, which is often used, a pass schedule is designed for each rolled material. When rolling various types of plates (plate thickness, plate width, steel type), it is inefficient to have one pass schedule with such a method for each type, so group the pass schedule and set it This group is called stratification. Within each stratification, for example, a value called logarithmic strain is set in a table, and the exit side plate thickness of a stand other than the final stand that is a pass schedule is defined. A table value is also provided for the tension between the stands.

The above determination method has a drawback that the pass schedules of a plurality of rolled materials are calculated on the basis of the same value even though the plate thickness, the plate width, and the deformation resistance are different within the same layer. Therefore, the method of designing the pass schedule for each rolled material as represented by Non-Patent Document 6 is not appropriate for the design for each layer.
In order to avoid this problem, it is possible to optimize the pass schedule for each rolled material, and to set the average value as the value of the pass schedule for each layer, but the thickness, width, Since variations such as deformation resistance are not taken into account, if the variation is large, the solution of the pass schedule may not be obtained, and the sensitivity of the rolling load and motor current to the change in deformation resistance is high and robust. In some cases, it was a pass schedule with no sex.

Further, at the time of rolling, even if the same plate thickness, the same plate width, and the same steel type are used, there are variations in the rolling state, for example, variations in friction and deformation resistance of the rolled material. However, since the design method for each rolled material is designed using a rolling model assuming that there is no variation, the obtained pass schedule is likely to be a non-robust pass schedule due to such variation. . If the variation is large, the optimal solution for the path schedule may not be obtained.
Considering the above, it is clear that a highly reliable pass schedule can be designed if the rolling pass schedule is determined in consideration of variations such as plate thickness, width, and deformation resistance. However, it is not easy to select the design method.

  For example, when the above-described “optimization problem with constraints” is adopted, the actual data to be used (the input amount in the rolling mill, the pass schedule as the design parameter, the output amount) is one, so the thickness, It is difficult to reflect variations in the amount of rolling state such as sheet width, friction, and deformation resistance of the rolled material. In addition, when the method of “optimization problem assuming a probability distribution function” is adopted, variation can be taken into consideration by providing a constraint condition, but selection of a probability distribution that can reflect variation in the rolling state amount is possible. It will be extremely difficult. In addition, it is often difficult to determine the probability distribution when the number of data with variations is small.

  In other words, the reason why the variation effect cannot be absorbed by these determination methods is that only one actual data is used or a probability distribution function different from the actual data is assumed and used as a constraint condition. it is conceivable that. From this, it is considered that the influence of variation can be reduced by reflecting a plurality of performance data in the constraint condition in the optimization problem. It is also effective to prepare a plurality of constraint conditions.

Therefore, in view of the above problems, the present invention provides a rolling mill with a rolling pass schedule as a design parameter, the actual value of the input amount in two or more data of the rolling mill and / or the actual value and the rolling model. One or a plurality of constraint conditions using the predicted value of the output amount calculated from the above are set, and a rolling pass schedule for determining the delivery side plate thickness so as to minimize or maximize the evaluation function under the constraint conditions The purpose is to provide a decision method.
In addition, an object of the present invention is to provide a design parameter optimum value determination method that generalizes the determination method.

In order to achieve the above object, the present invention takes the following technical means.
That is, the technical means according to the present invention sets an evaluation function including at least one of a design parameter and an output amount of the design object for the design object having the design parameter, and uses the evaluation function to In the design parameter optimum value determination method for determining a design parameter, two or more pieces of data having actual values of the input amount to the design target are prepared, and the actual value of the input amount included in the data and / or the input amount The predicted value of the output amount calculated from the actual value and the design target model obtained by modeling the design target is obtained, and one or more constraint conditions using the actual value of the input amount and / or the predicted value of the output amount are set. The design parameter is determined so as to minimize or maximize the evaluation function under the constraint condition.

  According to this technical means, since the optimum value can be determined using the constraint condition using the actual data as it is, the optimum value (optimum solution) of the design parameter suitable for the actual result can be obtained. In addition, it is possible to design with the same procedure when the number of actual data is small or large. In addition, since the variation is not defined by the assumed probability distribution, it is possible to set a constraint condition suited to the actual situation even when the number of data is small. This is particularly effective when the distribution of the input quantity has two or more peaks and cannot be converted into a single peak distribution such as a normal distribution.

Preferably, the constraint condition is defined by a relational expression indicating that a ratio between the number of the data satisfying a predetermined condition and the number of all data is a reliability rate, and the reliability rate satisfies a predetermined value. .
By doing so, the constraint condition can be quantitatively evaluated as a reliability rate.
Further, it is preferable to apply a differentiable monotonically increasing function to the constraint condition and set a new constraint condition using the differentiable monotone increasing function.
By doing so, the constraint condition can be differentiated, and an optimization method using differentiation can be used. For example, a sequential quadratic programming method (SQP) can be used, and the optimization calculation is speeded up and highly accurate.

Further, it is preferable to set a constraint condition using an assumed value of the input quantity instead of the actual value of the input quantity, and to determine the design parameter under the constraint condition.
Thus, even when the actual value of the input amount cannot be used, the design parameter optimum value determination method according to the present invention can be used.
Note that it is very preferable to correct the design target model by using data including input values, output amounts, and actual values of design parameters in the design target.
By doing so, the accuracy of the optimum solution obtained is increased by increasing the accuracy of the model to be designed.

When the optimum design parameter determination method described above is used, if the optimum design parameter cannot be solved, it is possible to loosen at least one of the constraints so that the design parameter can be solved. Highly preferred.
By doing so, the design parameters can be obtained reliably under any constraint conditions.
In the case where the optimum design parameter determination method described above is applied to the determination of the rolling pass schedule, at least one of the design parameters and the output amount of the rolling mill is applied to the rolling mill having the pass schedule as the design parameter. In the rolling pass schedule determination method of setting an evaluation function including and determining the pass schedule using the evaluation function, two or more rolling data having actual values of the input amount to the rolling mill are prepared, and the rolling data A predicted value of the output amount calculated from the actual value of the input amount and / or the actual value of the input amount and the rolling model obtained by modeling the rolling mill, and the actual value of the input amount and / or the output It is preferable to set one or a plurality of constraint conditions using the predicted value of the competence, and determine the path schedule so as to minimize or maximize the evaluation function under the constraint conditions.

By doing so, since the optimum value can be determined using the constraint condition using the actual rolling value as it is, the optimum solution of the pass schedule that matches the actual result can be obtained. That is, it is possible to design an optimal path schedule that satisfies equipment constraints, stable operation constraints, quality constraints, and productivity constraints. In addition, it is possible to design with the same procedure when the number of rolling record data is small or large.
In addition, since the assumed probability distribution is not used for the constraint condition, it is possible to set the constraint condition in accordance with the actual situation even when the number of rolling record data is small. This is particularly effective when the distribution of the actual value of the input amount has two or more peaks and cannot be converted into a distribution of one peak such as a normal distribution.

Preferably, the constraint condition is defined by a relational expression indicating that the ratio between the number of rolling data satisfying a predetermined condition and the total rolling data is a reliability rate, and the reliability rate satisfies a predetermined value. Good.
By doing so, the constraint condition can be quantitatively evaluated as a reliability rate.
In the case where the rolling mill includes a plurality of rolling stands, the evaluation function includes a rolling reduction ratio, a rolling load, a motor current, an entry side tension, an exit side tension in the rolling mill, and rolling. It is preferable to include at least one of the tension between the stands and the thickness of the exit side of the rolling stand other than the final rolling stand.

  By carrying out like this, each reduction ratio in each rolling stand, rolling load, motor current, entry side tension in a rolling mill, exit side tension, tension between rolling stands, exit side plate thickness in rolling stands other than the final rolling stand A pass schedule that can be optimized can be determined. By optimizing the delivery side thickness and rolling reduction, the rolling balance can be improved and stable operation is possible. By optimizing the tension between the stands and the entrance and exit side tensions of the rolling mill, stable operation is possible. By optimizing the load, it is possible to prevent meandering of the rolled material, improve shape quality, and operate stably. By optimizing the motor current, productivity can be improved and stable operation can be achieved.

In addition, it is preferable to apply a monotonically increasing function to the constraint condition to obtain a new constraint condition using the differentiable monotone increasing function.
By doing so, the constraint condition can be differentiated, and an optimization method using differentiation can be used. For example, sequential quadratic programming can be used, and optimization calculation is speeded up and highly accurate.
In addition, it is preferable that a constraint condition is set using an assumed value of the input amount instead of the actual value of the input amount, and a path schedule is determined under the constraint condition.

By doing so, for example, even when the rolling mill before construction or remodeling of the rolling mill does not exist and there is no rolling mill to be designed, and the performance data cannot be used, the optimum design of the pass schedule becomes possible. Furthermore, it is possible to optimally design a pass schedule even for a rolled material of an unproven sheet thickness, width, and steel type, and it is possible to design a pass schedule for a new material.
Moreover, it is very preferable to correct the rolling model using data consisting of actual values of the input amount, output amount and pass schedule in the rolling mill.
Thereby, the precision of the rolling pass schedule obtained becomes high by making a rolling model highly accurate.

When using the rolling pass schedule determination method described above, if the optimum pass schedule cannot be solved, it is very preferable to loosen at least one of the constraints so that the pass schedule can be solved.
In this way, an optimum rolling pass schedule can be reliably obtained under any constraints.
The pass schedule described above may be the exit side plate thickness and / or the tension between the rolling stands at a rolling stand other than the final rolling stand.

If only the exit side plate thickness of the rolling stand is used as a pass schedule, a pass schedule that does not change the tension between the stands can be obtained, and if only the inter-stand tension is used as the pass schedule, a pass schedule that does not change the stand exit side plate thickness can be obtained. When both are set as pass schedules, a pass schedule for changing both the exit side thickness of the rolling stand and the tension between the stands is obtained.
The selection of the variable for the pass schedule may be determined in consideration of the rolling balance and stable operation. For example, when emphasizing stable operation, only the exit side plate thickness of the rolling stand may be used as the pass schedule. Moreover, when it is desired to reduce the amount of change of the pass schedule by optimization, both the exit side plate thickness of the rolling stand and the tension between the stands may be used as the pass schedule.

  It should be noted that the exit side plate thickness of the rolling stands other than the final rolling stand includes a reduction rate, logarithmic strain, and the like, that is, an amount uniquely derived from the exit side plate thickness of the rolling stand. Further, when the entry side / exit side tension of the rolling mill can be changed, the tension between the stands can be optimized including the entry side / exit side tension.

According to the design parameter optimum value determination method according to the present invention, by preparing one or a plurality of constraint conditions reflecting two or more actual data, the influence of the variation in the rolling state is minimized, and the design parameter is optimized. The value can be obtained with high accuracy and high speed.
In particular, in determining the rolling pass schedule, it is possible to obtain a highly accurate and reliable rolling pass schedule at high speed, reducing the burden on the operator, maintaining stable operation, improving the dimensional accuracy of the rolled material, and improving productivity. It can contribute to improvement.

Hereinafter, a method for determining optimum values of design parameters according to the present invention will be described with reference to the drawings.
Design objects for obtaining the optimum values include a rolling mill having a rolling pass schedule described in the following examples as a design parameter, a cooling device having a cooling water amount as a design parameter, and a structure having a member dimension as a design parameter. There are a number of possible parts such as machine parts and the like, but in the embodiment described below, there is no particular limitation and it is a design object.
These design objects have design parameters, and an optimum function is set by setting an evaluation function including at least one of the design parameters and output amount of the design object, and determining the design parameters using the evaluation function. I am trying to find a value.

[First Embodiment]
FIG. 1 shows a block diagram of a first embodiment of a setting parameter optimum value determination method according to the present invention.
First, the input amount u and the design parameter x input to the design target (control target) are input to the design target model G _PLANT that models the design target, and the output amount y is output. The input amount u is a variable that defines the state of the design target, and may include time. However, the design parameter x is excluded. Here, u, x, and y are scalars or vectors. The output amount y may include some or all of u and x.
The design target model is expressed by Expression (1), and is set by the model setting unit 1 in FIG.

Here, G _PLANT is a nonlinear model, but may be a linear model.
In the present embodiment, it is assumed that the model accurately approximates the design target, and the actual value of the input amount (also referred to as the actual input amount) is input to the design target model via the actual input amount input unit 2 in FIG. The output obtained by substituting for G _PLANT is used, and the actual output value (also called the actual output amount) is not used.
In order to obtain the optimum value of the design parameter x, an evaluation function is set by the evaluation function setting unit 3 in FIG. Specifically, the evaluation function is determined as in Expression (2), where N is the number of actual input quantities.

_{Here, J j (u j, y} j, x) is the j th input quantity u _j, the output quantity y _j, the function consisting of the design parameters x, a part of the evaluation function J, for example, as a quadratic form It is given by equation (3). Since x is the same regardless of the input amount and the output amount, there is no subscript j.
In the present embodiment, y _j is calculated from the input amount, the design parameters, and the design target model using Expression (1).
Further, the "data" of the present embodiment, consists of an input quantity u _j or output quantities y _j or design parameter x, is that a set of values including at least input quantity u _j. The input quantity u _j and the output quantity y _j constituting this data may be actual values or predicted values. Further, the design parameter x may be an actual value or a value during calculation.

When y _j or x is a scalar, the matrix Y or X is a scalar. Note that J _j (u _j , y _j , x) is not limited to the quadratic form, and may be another linear or non-linear expression.
Further, m is the number of “predetermined conditions” that are the constraint conditions in the conventional optimization problem, and such conditions are expressed with a reliability rate.
The preset condition (constraint condition in the conventional optimization problem) is expressed by Expression (4) and Expression (5).

  In the present embodiment, the ratio of the data satisfying the conditions such as Expression (4) and Expression (5) to all data is defined as the reliability rate. That is, the reliability rate is expressed by Equation (6).

Then, a threshold value corresponding to the _kth condition g _k (u, y, x) ≧ 0 (threshold value of the reliability rate, which may be simply referred to as a reliability rate) is _defined as R _k (k = 1,. .., M) and the constraint conditions in this optimization problem are defined as shown in Equation (7). Such constraint conditions are set by the constraint condition setting unit 4 in FIG. As can be seen from k = 1,..., M in Expression (7), there may be one constraint condition or a plurality of constraint conditions.

When performing a highly accurate optimum design that matches the actual results using the equations defined above, first, the actual input amounts u _j (j = 1,..., N) are represented by the design target model of the equation (1). , The output amount y _j (j = 1,..., N) is calculated, and the evaluation function of equation (2) is minimized under the constraint condition (constraint condition) of equation (7). Solving the problem will help. This calculation is performed by the reliability factor optimization unit 5 of FIG.
In this way, all the actual input quantities (multiple actual input quantities) are used instead of the stochastic optimal value determination method in which constraints are set using conventional probability distributions, taking into account variations. It is possible to perform a deterministic optimal value determination method using.

Here, as a specific solution of the optimum value determination method, for example, an enumeration method can be used. The enumeration method is a solution method for calculating all combinations in the combination optimization problem and obtaining an optimal solution from those calculations. Specifically, this calculation is performed by the nonlinear optimization problem solving unit 6 of FIG.
When the optimization calculation is actually performed in order to obtain the optimum value, the optimum design parameter may not be obtained because the constraint condition is too strict. Therefore, the solvability determination unit 7 in FIG. 1 determines whether or not the reliability rate set by the constraint condition (formula (7)) is too strict. For example, the solvable determination unit 7 has a function of determining whether or not the calculation converges with a predetermined number of calculation steps and calculation time.

When the solvability determining unit 7 determines that the solvability is not solvable, a signal is sent to the reliability rate changing unit 8 in FIG. 1, and the reliability rate changing unit 8 gradually decreases the reliability rate R _k , and again the nonlinearity. The optimization problem can be solved by advancing the calculation in the optimization problem solving unit 6. For example, when the initial reliability rate is 0.7, if it is not solvable, it is decreased by 0.1 to 0.6, 0.5,. When the reliability rate is 0, the constraint condition becomes invalid, and an optimization problem without the constraint condition is obtained, so that the solution can be obtained.
Here, to all trust rate R _k may be reduced uniformly, priority within the confidence factor R _k a (priority) provided, high priority reliable rate R _k maintains the value to be satisfied, Others may be reduced. In this case, the constraint corresponding to the maintained reliability rate R _k is emphasized, and the constraint corresponding to the reduced reliability rate is not emphasized. Note that the reduction rate of the reliability rate R _k may be changed according to the restriction.

Note that by going trust rate R _k is gradually increased, may be adopted maximum confidence factor R _k is solvable. Here, gradually increasing or decreasing the reliability rate R _k includes calculating all the combinations and searching for the reliability rate R _k that matches the constraint condition.
The optimum design parameters obtained by the calculation in the reliability factor optimization unit 5 described above are output via the optimization result output unit 13.
Specific examples will be described in order to deepen the understanding of the optimum value determination method described above.
The design target model, evaluation function, and constraints are defined as follows.

In this example, the reliability is set to R ₁ = R ₂ = R ₃ = R ₄ = 1.0, and the design parameters are limited to be in the range of 0-1. Then, y is a probability that is 0.4 or more and 0.6 or less, and a value that maximizes R ₅ = R ₆ is determined.
Here, x ₁ = 0.0, 0.1, 0.2,..., 1.0, x ₂ = 0.0, 0.1, 0.2,. The evaluation function and the constraint condition are calculated for all combinations of x ₁ and x ₂ . Accordingly, since the search is performed within the range of the constraint conditions of x ₁ and x ₂ , the constraint conditions of x ₁ and x ₂ are automatically satisfied. Then, among all the combinations of x ₁ and x ₂ , the largest one of the reliability rates that satisfy the constraint condition regarding y is selected.

The specific calculation was performed as follows.
First, the reliability rate R ₅ = R ₆ for y is set to 1, and all combinations are examined to check whether all constraint conditions are satisfied.
If even one of them is not satisfied, the reliability rate R ₅ = R ₆ is decreased by 0.1, and all the combinations are examined again to check whether all the constraint conditions are satisfied. As a result, when x ₁ = 0.4, 0.5, the maximum is R ₅ = R ₆ = 2/3 = 0.67 ≧ 0.6.
Furthermore, within the range of x ₁ = 0.4, 0.5, when _{x 1 = 0.5, x 2 =} 0.5, y 1 = 0.4, y 2 = 0.55, y 3 = 0.65, and the value of the evaluation function is 0.035, which is the minimum value. Therefore, these x ₁ and x ₂ are optimum solutions.

The same problem can be solved when there are three or more design parameters.
In addition, in order to increase the solution accuracy of the design parameter, the step of discretization of the design parameter x may be reduced. In this case, a branch and bound method (see Applied Mathematical Planning Handbook, Mikio Kubo, Akihisa Tamura, Tomomi Matsui, 2002, Asakura Shoten, p. 267) can be used to reduce the amount of calculation. The branch and bound method is not to search all of the branches enumerated by the enumeration method, but is limited to a part, thereby speeding up. The optimization method is not limited to these methods, and other methods such as a simulated annealing method and a tabu search method may be used.

FIG. 2 is a flowchart showing the calculation procedure described above.
First, an actual input amount of two or more data is fetched, a design target model is fetched, a constraint condition for evaluating a reliability rate is set, and an evaluation function is set. Next, the optimization problem with constraints is solved using all input quantities, and when the solution cannot be obtained, the reliability is changed and the optimization problem is solved again. If a solution is obtained, the process ends.

[Second Embodiment]
Next, a second embodiment of the design parameter optimum value determination method according to the present invention will be described.
Although this embodiment is almost the same method as the first embodiment, it is greatly different in that the design target model is corrected with the actual input / output amount.
FIG. 3 shows a block diagram when the design target model is corrected with the actual input / output amount. As can be seen from comparison with FIG. 1, an actual output amount input unit 9 for taking in an actual output amount and a model correction unit 10 for correcting a design target model are provided.
Using the actual input / output amount, the model correction unit 10 corrects the design target model for each data.

For example, the actual input quantity, design parameter, and output quantity are u _{j_actual} , x _{j_actual} , y _{j_actual} , and the calculated output quantity using the design target model is y _{j_calculated} = G _PLANT (u _{j_actual} , x _{j_actual} ) In some cases, the model correction unit 10 can correct the slope of the equation (1) as follows.

また、式（９）の如く切片を変更してもよい。

Further, the intercept may be changed as shown in Equation (9).

Both the inclination and the intercept may be changed by reflecting the ideas of Expressions (8) and (9) at the same time, or a new parameter may be provided in the design target model for non-linear correction.
In the case of optimization calculation, the accuracy of the optimal solution can be increased by using a model corrected for each data.
The design target model and the input / output amount in this embodiment are as follows, and the evaluation function and the constraint conditions are substantially the same as those in the first embodiment.

In the optimization calculation, in calculating the y _1, y _2, y ₃ from u _1, u _2, u _3, by using the above modified design object model, high design object model before correction is As a result, the accuracy of the optimum solution obtained is increased.
FIG. 4 shows a flowchart of this embodiment.
First, the actual input / output amount of two or more data is taken in, and the design target model is corrected for each data using the actual input / output amount for each data. Next, the modified design target model is taken in, a constraint condition for evaluating the reliability rate is set, and an evaluation function is set. After that, the optimization problem with constraints is solved using the total input amount and the model corrected for each data. If no solution is obtained, the reliability is changed and the optimization problem is solved again. If a solution is obtained, the process ends.

[Third Embodiment]
Next, a third embodiment of the design parameter optimum value determination method according to the present invention will be described.
Although this embodiment is almost the same method as the first embodiment, it adopts a differentiable monotonically increasing function with a constraint condition using a plurality of performance data as an input variable, and this adopted differentiable monotonic function. The difference is that the increase function is a new constraint. By doing so, an optimization algorithm using differential coefficients such as sequential quadratic programming (SQP) can be applied.
FIG. 5 shows a block diagram of the present embodiment. As can be seen from comparison with FIG. 1, a function setting unit 11 that sets a differentiable monotonically increasing function and a constraint condition approximation that approximates a constraint using a differentiable monotonically increasing function set by the function setting unit 11. Part 12.

Specifically, the left side of the constraint condition (Expression (7)) set by the constraint condition setting unit 4 takes a discrete value and cannot be differentiated. For this reason, the calculation method using the differential coefficient of the constraint condition cannot be used during the optimization calculation as in the case of sequential quadratic programming. On the other hand, the sequential quadratic programming method is an algorithm that can solve a nonlinear optimization problem with constraints at high speed and with high accuracy, and it should be usable.
Therefore, first, the function setting unit 11 sets a monotonically increasing and differentiable function (that is, a non-decreasing differentiable function) such that 0 at −∞ and 1 at + ∞. For example, a sigmoid function like Formula (10) is set. The sigmoid function is shown in FIG.

As long as it is a monotonically increasing function that can be differentiated, it is not limited to a sigmoid function, and other functions such as an arctangent function (tan ⁻¹ (ξ)) may be used.
Then, the constraint condition approximating unit 12 applies the expression (10) to the original constraint condition as an approximate constraint condition (expression (11)).

Here, the confidence factor R _k of the formula (11), a approximate confidence rate R _k of Equation (7), and solving the optimization problem approximate under conditions satisfying the confidence factor Become. The change of x appears continuously in the function value of the constraint condition, and the optimization calculation can be performed.
For the optimization calculation, a steepest descent method, a Newton method, or the like can be used in addition to the above-described sequential quadratic programming method.
For example, when N = 1, Equation (7) satisfies the constraint g _k (u _j , y _j , x) ≧ 0 when R _k = 1, but in Equation (11), R _k ≧ 0. In the case of 5, the constraint g _k (u _j , y _j , x) ≧ 0 is satisfied. Further, when N is an even number and N → ∞, in Expression (7), when R _k = 0.5, strictly N / 2 data is constrained g _k (u _j , y _j , x) ≧ 0. In Expression (11), about N / 2 data satisfies the constraint g _k (u _j , y _j , x) ≧ 0.

Although reliable index becomes approximate confidence factor, if you choose a sufficiently large beta _k in the sigmoid function, no practical problem. Size of beta _k in equation (11), the change of g _k with respect to when x has _{changed, sigmf (g k (u j} , y j, x), d k) to appear to changing, g _k Determined by considering the range of changes. That is, the sigmoid function in the range of variation of g _k with respect to smoothly change, and, in the end points of the range of variation of g _k with respect to, as long as the asymptotic to 0 or 1. For example, if −1 ≦ g _k ≦ 1, about β _k = 0.1 to 10, and if −0.01 ≦ g _k ≦ 0.01, about β _k = 10 to 1000. Good. If the reliability rate exceeds 0.5, the average value approximately satisfies the constraint.

Specific examples will be described in order to deepen the understanding of the present embodiment.
The design target model, evaluation function, and constraints are defined as follows.

In this specific example, the reliability is set so that R ₁ = R ₂ = R ₃ = R ₄ = 0.5, and the design parameters are in the range of 0-1. Then, y is a probability of 0.4 to 0.6, and a value that maximizes R ₅ = R ₆ is obtained.
For more information, while reducing the R ₅ = R ₆ in 1 0.1 increments, solved optimization problem with the above constraints by sequential quadratic programming. As a result, it became solvable when R ₅ = R ₆ = 0.6, and when x ₁ = 0.45 and x ₂ = 0.5, the value of the evaluation function was 0.027, which was the minimum. Therefore, these x ₁ and x ₂ are optimum solutions.

FIG. 7 shows a flowchart of a calculation method according to the present embodiment.
First, a record input amount of two or more data is fetched, a design target model is fetched, and a constraint condition for evaluating the reliability rate is set. Next, a non-decreasing differentiable function is set, and the constraint condition is approximated using this non-decreasing differentiable function. After that, an evaluation function is set, and the optimization problem with constraints is solved using the total input amount and the design object model. If no solution is obtained, the reliability is changed and the optimization problem is solved again. If a solution is obtained, the process ends.

[Fourth Embodiment]
Next, a fourth embodiment of the design parameter optimum value determining method according to the present invention will be described.
This embodiment is a method for determining optimum values of design parameters applied by combining the technique of the second embodiment (having the function of modifying the design target model) and the third embodiment (adopting a monotonically increasing function as a constraint). It is.
FIG. 8 shows a block diagram of the present embodiment. As can be seen from this figure, the configuration shown in FIG. 1 is further provided with an actual output amount input unit 9, a model correction unit 10, a function setting unit 11, and a constraint condition approximation unit 12.
FIG. 9 shows a flowchart of the calculation method according to the present embodiment.

First, the actual input / output amount of two or more data is taken in, the design target model is corrected using the actual input / output amount for each data, and the corrected design target model is taken in. Next, a constraint condition for evaluating the reliability rate is set. Furthermore, a non-decreasing differentiable function is set, and the constraint condition is approximated using this non-decreasing differentiable function. Thereafter, an evaluation function is set, and the optimization problem with constraints is solved using the total input amount and the design target model corrected for each data. If no solution is obtained, the reliability is changed and the optimization problem is solved again. If a solution is obtained, the process ends.
Since the operational effects are substantially the same as those of the second embodiment and the third embodiment, the description thereof is omitted.

[Fifth Embodiment]
Next, a fifth embodiment of the design parameter optimum value determination method according to the present invention will be described.
Although this embodiment is almost the same method as the third embodiment, it is greatly different in that the constraint condition is set using the assumed value of the input amount instead of the actual input amount.
FIG. 10 shows a block diagram of the present embodiment. As can be seen from comparison with FIG. 5, a predicted input amount input unit 14 for inputting an assumed value of the input amount is provided.
For example, when there is no actual input amount because there is no design target, and this method can predict the input amount from similar design targets and design conditions, an assumed value of the input amount is created based on the prediction. This is particularly effective when performing optimization by evaluating the reliability rate using the assumed input quantity. In addition, it is effective because it is possible to design a pass schedule even when a material of a sheet width, a sheet thickness, and a steel type having no rolling record is rolled.

As an example, if 73% of the input u is 0.8 and the rest is 1.1, u _j = 0.8 (j = 1,..., 73), u _j = 1.1 (J = 74,..., 100) may be used.
FIG. 11 shows a flowchart of the calculation method according to the present embodiment.
First, a predicted input amount belonging to two or more data is fetched, a design target model is fetched, and a constraint condition for evaluating the reliability rate is set. Next, a non-decreasing differentiable function is set, and the constraint condition is approximated using this non-decreasing differentiable function. After that, an evaluation function is set, and the optimization problem with constraints is solved using the total input amount and the design object model. If no solution is obtained, the reliability is changed and the optimization problem is solved again. If a solution is obtained, the process ends.

The example which applied 1st Embodiment described above to the pass schedule determination of the cold tandem rolling mill 20 which rolls a thin steel plate is described.
As shown in FIG. 12, the thin steel plate is manufactured by introducing a rolled material 21 as a base into a tandem rolling mill 20 provided with a plurality of rolling stands 22 and continuously rolling. The rolled material 21 (finished plate) exiting the rolling stand 22 provided in the final stage is wound up by a coiler (not shown) which is a winder disposed on the downstream side in the transfer direction of the rolled material 21. It has become. Between each rolling stand 22, a plate thickness meter for measuring the plate thickness of the rolled material 21 and a plate speed meter for measuring the plate speed are provided as appropriate (both are not shown).

12 schematically shows the cold tandem rolling mill 20, and includes five rolling stands 22, that is, # 1 stand to # 5 stand. Each rolling stand 22 has, for example, a pair of work rolls 23, an intermediate roll 24, and a backup roll 25 for rolling the rolled material 21. The rolled material 21 (raw material) introduced into the # 1 stand is rolled at a predetermined reduction ratio, transferred to the rolling stand 22 on the downstream side, and finally rolled at the # 5 stand on the most downstream side. It becomes a finishing board.
The tandem rolling mill 20 has a pass schedule design device 26 (control unit) that designs how to reduce the rolling reduction ratio and tension between the stands 22. The path schedule design device 26 implements the design parameter optimum value determination method described in the first embodiment, and includes an actual input amount input unit 2, a path schedule optimization unit 5A, a constraint condition setting unit 4, and an evaluation. It has the function setting part 3 and the rolling model setting part 1A. The path schedule optimization unit 5 </ b> A includes a nonlinear optimization problem solving unit 6 (a nonlinear optimization problem solving unit 6 with constraints), a solvability determination unit 7, and a reliability rate changing unit 8.

The pass schedule design device 26 is realized in the form of a program on an off-line computer or on-line process computer or PLC of the tandem rolling mill 20. Here, as shown in FIG. 12, the pass schedule design device 26 does not necessarily have to be connected online with the plate thickness / tension control device 16 or the rolling stand 22 itself, and the actual input amount, the target plate thickness, and the target tension. As long as it can be exchanged at least offline.
From the pass schedule design device 26, the target plate thickness at each rolling stand 22 and the target tension between each rolling stand 22 are output, and each rolling stand is connected via a plate thickness / tension control device 16 constituted by a sequencer or the like. 22 applies.

The rolling pass schedule determination method (design parameter optimum value determination method) performed in the pass schedule design device 26 is as follows.
As described above, the pass schedule is the exit side plate thickness and / or the inter-stand tension of a rolling stand other than the final rolling stand. Hereinafter, a case will be considered where the exit side plate thickness of a rolling stand other than the final rolling stand is handled as a pass schedule. At this time, the tension between the stands is used as the input value as it is, or is partially changed and used as a fixed value.
In addition, when handling the tension between the stands as the pass schedule, or when handling both the exit side plate thickness of the rolling stand other than the final rolling stand and the tension between the stands, the pass schedule is determined for the rolling stands other than the final rolling stand. Since the design can be performed in the same manner as in the case of handling the delivery side plate thickness, the following embodiments do not limit the meaning of the pass schedule.

For each rolled material 21, H _i is the #i stand entry side plate thickness, h _i is the #i stand exit side plate thickness, and r _i is the #i stand reduction rate. The original plate thickness is expressed as H ₁ or h ₀ .
First, the relationship between the rolling reduction and the plate thickness is as shown in Equation (12).

The input amount to the rolling model is the original plate thickness, finish plate thickness, plate width, rolling mill entry side tension, rolling mill exit side tension, element component amount, roll roughness, and rolling length in the same roll. Think about it. These are variables for uniquely determining the rolling state. However, design parameters to be optimized which will be described later are excluded.
As the output amount, a rolling load (line load) and a motor current (current of a motor that drives a rolling stand) are considered. The line load is a rolling load per unit width of the rolled material 21. In place of the motor current, motor power or motor power may be employed.

  The relationship between the input amount, the output amount, and the optimized design parameter is related by the rolling model set by the model setting unit 1. In the case of a present Example, Formula (13)-Formula (15) is employ | adopted as a rolling model.

  Here, as a model indicating the relationship between the rolling load and the motor current, Expression (16) and Expression (17) are employed. (Refer to "Theory and practice of plate rolling", edited by Japan Iron and Steel Institute (1984) pp. 112-113)

  Now, let N be the number of rolling materials 21 in the stratification to which the same pass schedule is applied, that is, the number of rolling performance input amounts. In addition, the relationship between the exit side plate thicknesses at the respective stands is expressed by the equations (18) and (19).

Thereby, each stand exit side plate | board thickness of the rolling material 21 in the same layer from which original board thickness and finishing board thickness differ can be determined with a common parameter. This relational expression may be different.
Hereinafter, in order to simplify the story as described above, consider a case where only the exit side plate thickness of the stands other than the # 5 stand (final stand) is used as an input variable. Even when the tension between the stands is an input variable, it can be solved in the same manner only by increasing the number of input variables.

  First, out of the N pieces of data, the thickness of the exit side of the # 1 stand to # 4 stand of one representative rolled material 21 is selected as a design parameter as shown by the equation (20).

Incidentally, the thickness _{[h j, 1, h j} , 2, h j, 3, h j, 4] T of the other of the rolled material 21, equation (18), the equation (19),

Can be obtained.
u and y are the same as in equations (13) and (15), and there are N pieces of data, respectively.
The evaluation function is determined as shown in equations (22) and (23).

This example is merely an example, and other variables can be selected, and other nonlinear evaluation functions including exponential functions and division are also possible. For example, a term of the square of the current difference between adjacent stands can be added. Similarly, the evaluation function can include the case where the plate thickness is used instead of the rolling reduction, and the case where torque or power is used instead of the current. The advanced rate and the position of the neutral point can also be included in the evaluation function.
Furthermore, the number of preset conditions (conventional constraint conditions) is set to m, and as an example, the conditions are determined as in Expression (24) to Expression (37).

g _{1 to} g ₆ and g ₁₂ are constraints for preventing meandering and shape deterioration due to inappropriate rolling load, and for equipment protection. Upper and lower limits are determined from past performance and knowledge.
_{g 7 ~g 11, g 13 ~g} 17 is a current limitation for the rolling mill motor protection.
g ₁₈ ~g ₂₁ is a constraint in order to ensure the balance of the reduction ratio, the reduction rate margin at the lower limit value and the adjacent stand each other of the reduction ratio of the final stand in the original, from past experience and knowledge decide.

Here, the selection method of the ideal rolling variable value is arbitrary. For example, if the value of the rolling state before optimization is used, a pass schedule close to the rolling state before optimization can be obtained. The rolling state of the rolled material 21 having similar properties such as deformation resistance can also be used. If the ideal rolling variable value is set to a new ideal value that is different from that before optimization, a pass schedule that realizes the rolling state of the new ideal value can be obtained. In addition, the ideal load value of the specific rolling stand 22 can be used as a new ideal value, and the ideal load value of other stands can be used as the actual load value before optimization.
In the case of this example, the ideal rolling variable value, the upper and lower limit values, and the ideal deviation were determined based on the operator's knowledge about the tandem rolling mill 20 and past rolling results.

  Of the total data, the ratio of the number of data satisfying each constraint condition in the case of the design parameter x is defined as the reliability rate as expressed by the equation (38).

Here, n (g _k (u, y, x) ≧ 0) indicates the number of data satisfying the condition of g _k (u, y, x) ≧ 0 among all data N.
When the reliability threshold corresponding to the k-th constraint (which may be simply referred to as a reliability) is set as R _k and the reliability satisfying each constraint is determined, the constraint for evaluating the reliability is It becomes like this. However, R _k is a real number of 1 or less.

From the above, in order to perform a highly accurate optimum design that matches the actual results, the actual input amounts u _j (j = 1,..., N) and the rolling model of the equation (17) are used. Under the constraint conditions of Expressions (37) and (39), an optimization problem that minimizes the evaluation function of Expression (22) is solved.
The enumeration method was used as a solution to the optimization problem. Specifically, for example, when the rolled material 21 is rolled from 2.8 mm to 1.4 mm, the design parameters are _four , x = [x ₁ , x ₂ , x ₃ , x ₄ ]. 1.4 <x _i <2.8 (i = 1,..., 4). As an example, x _i = 1.40, 1.414, 1.428,..., 2.786, 2.800 are discretized in increments of 1/100, and all combinations of x ₁ to x ₄ are restricted. The solution that satisfies the condition is selected to minimize the evaluation function.

Here, when it is desired to reduce the calculation amount for determining the optimum value, the branch and bound method can be used as described above. The optimization method is not limited to these methods, and other methods such as a simulated annealing method and a tabu search method may be used.
However, there is a case where the optimization problem cannot be solved (when the calculation does not converge even if the calculation is advanced). This is a case where the constraint condition is too strict, that is, the set reliability rate is too large. Whether or not such a situation exists is determined by the solvable determination unit 7 of FIG. When the solvability determination unit 7 determines that the situation is not in the solvable state, the reliability rate change unit 8 gradually decreases the reliability rate R _k to make the optimization problem solvable. it can.

  In the reliability rate changing unit 8, two types of reliability rates are provided as shown in equations (40) and (41).

The R _A as a reference trust rate, to determine the relationship R _A and R _B as in FIG. 13.
As initial values, R _A and R _B are decreased until a solution is obtained from R _A = 1.0. For example, decrease by 0.1 until a solution is obtained. In the present embodiment, when the standard reliability rate becomes −1.0, the constraint condition becomes invalid and becomes equivalent to an optimization problem without the constraint condition, so that the solution can always be obtained.
Here, when obtaining the case of the maximum reliability rate at which a solution can be obtained, the reliability rate may be increased until the solution is obtained, or other optimizations such as bisection method, sequential quadratic programming method, etc. A method may be used and is not limited to the present method. Also, some of the reliability ratios R _k may be constant regardless of changes in the reference reliability ratio. For example, if a constant value of R _k = 0.5 is set, the average value almost satisfies the constraint. The method of determining the reliability rate according to the constraint condition is not limited to the present embodiment.

Here, a constraint corresponding to a large value reliability is emphasized, and a constraint corresponding to a small value reliability is not designed. In the present embodiment, emphasis is placed on the restrictions on the relationship between the rolling load of the # 1 stand and the reduction ratio, and the constraints on the relationship between the rolling load of the # 5 stand and the reduction ratio are not emphasized.
As a result of the above calculation, a reliability rate of R _A = 0.4 and R _B = 0.7 is obtained. As optimal solutions, x ₁ = 2.338, x ₂ = 1.946, x ₃ = 1. 666, x ₄ = 1.470 was obtained.
FIG. 14 is a flowchart showing the procedure of the rolling pass schedule determination method described above.

  First, a rolling record input amount of two or more rolling data is fetched, a rolling model is fetched, and a constraint condition for evaluating the reliability rate is set. In addition, an evaluation function is set. Next, the optimization problem with constraints is solved using the total input amount of rolling, and when the optimum pass schedule is not obtained, the reliability is changed and the calculation is performed again. If a solution is obtained, the process ends.

Next, the example which applied 2nd Embodiment mentioned above to the pass schedule determination of the cold tandem mill 20 which rolls a thin steel plate is described. The configuration of the tandem rolling mill 20 is substantially the same as that of the first embodiment.
FIG. 15 shows a block diagram of the present embodiment. That is, in the case where the actual output amount input unit 9 and the rolling model correction unit 10A are provided, and the rolling model is corrected by using the actual rolling output input / output amount input via the actual output amount input unit 9 in the rolling model correction unit 10A. It is.
For example, the rolling record of input quantity, design parameters, and output quantity is u _{j_actual} , x _{j_actual} , y _{j_actual} , and the calculated value of output quantity using the design target model is y _{j_calculated} = G _PLANT (u _{j_actual} , x _{j_actual} ) If it is, it can be corrected as shown in Equation (42) or Equation (43).

FIG. 16 shows a flowchart of the technique of FIG.
First, a rolling record input amount belonging to two or more rolling data is taken, and a rolling model is corrected for each data using a rolling record input / output amount. Next, the modified rolling model is taken in, a constraint condition for evaluating the reliability rate is set, and an evaluation function is set. Then, the optimization problem with constraints is solved using the total rolling input and the modified model. If the pass schedule cannot be obtained, the reliability rate is changed and the calculation is performed again. If a solution is obtained, the process ends.

Next, the example which applied the technique of 3rd Embodiment to the pass schedule determination of the cold tandem mill 20 which rolls a thin steel plate is described. The configuration of the tandem rolling mill 20 is substantially the same as that of the first embodiment.
FIG. 17 shows a block diagram of the present embodiment. A function setting unit 11 is newly provided in the path schedule design device 26, and a non-decreasing differentiable function is set by the function setting unit 11. Using this, an optimization algorithm such as sequential quadratic programming (SQP) can be applied.
First, in the function setting unit 11 (non-decreasing differentiable function setting unit), a function that can be differentiated by monotonically increasing that becomes 0 at −∞ and 1 at + ∞ is set. For example, the sigmoid function of Expression (44) is set.

  Then, the constraint condition approximating unit 12 shown in FIG. 17 approximates the constraint condition as shown in Expression (45) using the above function.

Here, the reliability rate R _k in equation (45) is an approximation of the reliability rate R _{k in} equation (39). For example, when N = 1, Equation (39) satisfies the constraint g _k (u, y, x) ≧ 0 at R _k = 1, but in Equation (45), when R _k ≧ 0.5. The constraint g _k (u, y, x) ≧ 0 is satisfied. In addition, when N is an even number and N → ∞, in Equation (39), exactly R / 2 data satisfies the constraint g _k (u, y, x) ≧ 0 when R _k = 0.5. However, in Expression (45), about N / 2 data satisfies the constraint g _k (u, y, x) ≧ 0.

In Equation (45), the magnitude of β _k is such that the change in g _k when x changes appears in the change in sigmf (g _k (u _j , y _j , x), d _k ). Determined in consideration of the range of change in g _k . In the case of this example, settings were made as follows.

FIG. 18 shows a flowchart of this embodiment.
First, a rolling record input amount of two or more rolling data is fetched, a rolling model is fetched, and a constraint condition for evaluating the reliability rate is set. Next, a non-decreasing differentiable function is set, and the constraint condition is approximated using this non-decreasing differentiable function. After that, an evaluation function is set, and a constrained optimization problem is solved using the total rolling input and rolling model. If no solution is obtained, change the confidence factor and proceed with the calculation again. If a solution is obtained, the process ends.

Next, the example which applied the technique of 4th Embodiment to the pass schedule determination of the cold tandem mill 20 which rolls a thin steel plate is described. The configuration of the tandem rolling mill 20 is substantially the same as that of the first embodiment.
FIG. 19 shows a block diagram of the present embodiment. A function setting unit 11 is newly provided in the path schedule design device 26, and a non-decreasing differentiable function is set by the function setting unit 11. Using this, an optimization algorithm such as sequential quadratic programming (SQP) can be applied. In addition, it has an actual output amount input unit 9 and a rolling model correction unit 10A. In the rolling model correction unit 10A, the rolling model is corrected using the rolling input / output amount input via the actual output amount input unit 9. .

FIG. 20 shows a flowchart of the method of this embodiment.
First, a rolling record input amount of two or more rolling data is fetched, a design target model is corrected for each data using a rolling record input / output amount, and a corrected design target model is fetched. Next, a constraint condition for evaluating the reliability rate is set. Furthermore, a non-decreasing differentiable function is set, and the constraint condition is approximated using this non-decreasing differentiable function. After that, an evaluation function is set, and the optimization problem with constraints is solved using the total rolling input and the corrected rolling model. If no solution is obtained, change the confidence factor and proceed with the calculation again. If a solution is obtained, the process ends.

Next, the example which applied the technique of 5th Embodiment to the pass schedule determination of the cold tandem mill 20 which rolls a thin steel plate is described. The configuration of the tandem rolling mill 20 is substantially the same as that of the first embodiment.
FIG. 21 is a block diagram of the present embodiment, and includes a predicted input amount input unit 14 for inputting an assumed value of the rolling input amount.
In the present embodiment, there is no tandem rolling mill 20 to be controlled yet and there is no actual rolling input, but when the rolling input can be predicted from similar design objects and design conditions, the predicted rolling input is input as the predicted input. The data is input to the path schedule optimization unit 5A via the unit 14.

FIG. 22 shows a flowchart of the method of this embodiment.
A rolling prediction input amount of two or more rolling data is taken in, a rolling model is taken in, and a constraint condition for evaluating the reliability rate is set. Next, a non-decreasing differentiable function is set, and the constraint condition is approximated using this non-decreasing differentiable function. After that, an evaluation function is set, and a constrained optimization problem is solved using the total rolling input and rolling model. If no solution is obtained, the reliability is changed and the optimization problem is solved again. If a solution is obtained, the process ends.
FIG. 23 shows the rolling record data when Example X is actually applied to the tandem rolling mill 20 and when it is not applied. The tension between the stands used the same value as before, and the exit side plate thickness of # 1 stand to # 4 stand, that is, the reduction ratio of # 1 stand to # 5 stand was optimized.

The set value of the reduction rate shown in FIG. 23C indicates the optimized reduction rate pass schedule. Note that the variation in rolling reduction is due to the difference in the original plate thickness and finish plate thickness of the rolled material 21 and operator intervention.
As a result of the optimization, the reduction ratios of the # 1 stand and # 5 stand were set to be small, and the ratio of entering the ideal values of the line loads of the # 1 stand and # 5 stand increased as shown in FIG. . In addition, as shown in FIG. 23B, the motor current and the reduction ratio balance were also optimized. In addition, the intervention by the operator was reduced, contributing to operational stability, and the out-of-tolerance length (off gauge) was reduced by 8% compared to the prior art.

The present invention is not limited to the above embodiment.
In other words, the tandem rolling mill has been described with an example having five stands, but the number of rolling stands is not limited to this, and the rolling form is not limited to cold rolling, and is also applicable to hot rolling. Is possible. Further, the present invention can be applied to a single stand mill such as a reverse rolling mill for rolling a thick steel material.

It is a block diagram of a 1st embodiment. It is a flowchart of a 1st embodiment. It is a block diagram of 2nd Embodiment. It is a flowchart of a 2nd embodiment. It is a block diagram of a 3rd embodiment. It is a figure which shows a sigmoid function. It is a flowchart of a 3rd embodiment. It is a block diagram of 4th Embodiment. It is a flowchart of a 4th embodiment. It is a block diagram of a 5th embodiment. It is a flowchart of a 5th embodiment. 1 is a block diagram of Example 1. FIG. It is the figure which showed a mode that the reliability rate was reduced so that it could be solved. 3 is a flowchart of the first embodiment. 6 is a block diagram of Embodiment 2. FIG. 10 is a flowchart of Example 2. 10 is a block diagram of Example 3. FIG. 10 is a flowchart of Example 3. FIG. 10 is a block diagram of Example 4. 10 is a flowchart of Example 4. 10 is a block diagram of Embodiment 5. FIG. 10 is a flowchart of Example 5. It is a figure which shows the rolling performance data when not applying with the case where the determination method of the rolling pass schedule concerning this invention is applied.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Model setting part 2 Actual input amount input part 3 Evaluation function setting part 4 Constraint condition setting part 5 Reliability rate optimization part 6 Nonlinear optimization problem solution part 7 Solvability judgment part 8 Reliability rate change part 9 Actual output amount input part 10 Model correction unit 11 Function setting unit 12 Restriction condition approximation unit 13 Optimization result output unit 14 Predicted input amount input unit 16 Plate thickness / tension control device 20 Tandem rolling mill 21 Rolled material 22 Rolling stand 26 Pass schedule design device 1A Rolling model setting Part 5A pass schedule optimization part 10A rolling model correction part

Claims (14)

An evaluation function including at least one of the design parameter and the output amount of the design object is set for the design object having the design parameter, and the design parameter is determined using the evaluation function. In the method
Prepare two or more data having the actual value of the input amount to the design object,
Obtaining a predicted value of the output amount calculated from the actual value of the input amount included in the data and / or the actual value of the input amount and a design target model obtained by modeling the design target;
One or more constraint conditions using the actual value of the input amount and / or the predicted value of the output amount are set,
A method for determining an optimum value of a design parameter, wherein the design parameter is determined so as to minimize or maximize an evaluation function under the constraint condition.   The constraint condition is defined as a relational expression indicating that the ratio of the number of data and the number of all data satisfying a predetermined condition is a reliability rate, and the reliability rate satisfies a predetermined value. The method for determining an optimum value of a design parameter according to claim 1.   3. A design parameter optimum value determining method according to claim 1 or 2, wherein a different monotone increasing function is applied to the constraint condition, and a new constraint condition using the differentiable monotone increasing function is obtained. .   The constraint parameter is set using an assumed value of the input quantity instead of the actual value of the input quantity, and the design parameter is determined under the constraint condition. Method for determining the optimum values of design parameters.   The design parameter optimization according to any one of claims 1 to 3, wherein the design target model is modified using data including input values, output amounts, and actual values of design parameters in the design target. Value determination method.   In using the design parameter optimum value determination method according to any one of claims 1 to 5, if the optimum design parameter cannot be solved, at least one of the constraint conditions so that the design parameter can be solved. A method for determining an optimum value of a design parameter, characterized by loosening one. An evaluation function including at least one of a design parameter and an output amount of the rolling mill is set for a rolling mill having the pass schedule as a design parameter, and the pass schedule is determined using the evaluation function. In the decision method,
Prepare two or more rolling data having the actual value of the input amount to the rolling mill,
Obtaining the predicted value of the output amount calculated from the actual value of the input amount included in the rolling data and / or the actual value of the input amount and a rolling model that models the rolling mill,
One or more constraint conditions using the actual value of the input amount and / or the predicted value of the output amount are set,
A method for determining a rolling pass schedule, wherein the pass schedule is determined so as to minimize or maximize the evaluation function under the constraint condition.   The constraint condition is defined as a relational expression indicating that the ratio of the number of the rolling data satisfying a predetermined condition and the total rolling data is a reliability rate, and the reliability rate satisfies a predetermined value. The method for determining a rolling pass schedule according to claim 7, wherein the rolling pass schedule is determined. The rolling mill comprises a plurality of rolling stands,
The evaluation function includes the rolling reduction at each rolling stand, rolling load, motor current, inlet side tension at the rolling mill, outlet side tension, and tension between rolling stands, and thickness of the outlet side at the rolling stand other than the final rolling stand. 9. The method for determining a rolling pass schedule according to claim 7 or 8, comprising at least one.   The method for determining a rolling pass schedule according to any one of claims 7 to 9, wherein a monotonically increasing function is applied to the restricting condition to obtain a new restricting condition using the differentiable monotonically increasing function.   The constraint condition is set using an assumed value of the input quantity instead of the actual value of the input quantity, and a path schedule is determined under the restriction condition. How to determine the rolling pass schedule.   The determination of the rolling pass schedule according to any one of claims 7 to 10, wherein the rolling model is corrected by using data including input values, output amounts, and actual values of the pass schedule in the rolling mill. Method.   When using the method for determining a rolling pass schedule according to any one of claims 7 to 12, if an optimal pass schedule cannot be solved, at least one of the constraint conditions so that the pass schedule can be solved. A method for determining a rolling pass schedule, characterized by loosening the wire.   The method for determining a rolling pass schedule according to any one of claims 9 to 13, wherein the pass schedule is an exit side plate thickness and / or a tension between rolling stands at a rolling stand other than the final rolling stand.

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