JPH1097302A - Method and device for automatically deciding model parameter - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make the time up to the decision of parameters of many models efficient and to reduce the burden on an operator by performing conversion into gene information having common upper and lower limits and calculating an evaluation function by using model parameters corresponding to gene information included in an individual body of a next generation obtained by performing a genetic processing utilizing the evaluation function. SOLUTION: Model operation is performed (102) by using an initial generation to extract a feature quantity such as a mean of model errors and a standard deviation. Evaluation functions are calculated by individual bodies of the initial generation (108). Then modem parameters are coded by using a relational expression to find gene information (110). A next generation is generated by performing a genetic processing (112). The found gene information of the next generation is coded by using the relational expression and put back to model parameters (114). Then a processing for a specific generation, e.g. 15th generation is performed (116) and when it is decided that a gene search ends, the processing ends.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for automatically determining model parameters, and more particularly, to a control model including a large number of model parameters, such as a finishing mill temperature drop model in a hot rolling mill. Minimizing a predetermined cost function, suitable for use in determining parameters,
The present invention relates to a method and an apparatus for automatically determining model parameters capable of automatically determining a large number of model parameters.

[0002]

2. Description of the Related Art Conventionally, when determining parameters such as a finish mill temperature drop model and a deformation resistance model in a hot rolling mill, the model is calculated by trial and error until the model calculation result and the measured data are accurately matched. Parameters were determined.

[0003]

However, in the conventional method, since the model parameters are determined by trial and error, there is a problem that it takes a long time to determine the parameters and the load on the person who adjusts is large. .

[0004] In recent years, the model structure has become complicated and the number of parameters to be determined has increased due to the increase in the accuracy of the model, and the time required for determining model parameters and the load on humans have been long and large.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned conventional problems. By using a genetic algorithm, the time required to determine the parameters of a control model having a large number of model parameters can be made more efficient. The task is to reduce the load.

[0006]

According to the present invention, when determining a large number of model parameters for minimizing a predetermined evaluation function, each model parameter is determined according to its absolute value level and a theoretically possible range. It encodes and converts it into genetic information having a common upper and lower limit, and performs genetic processing using the evaluation function on an individual which is a combination of the genetic information to obtain a next generation individual, The present invention solves the above problem by decoding the genetic information included in the individual and returning the decoded model parameters to the corresponding model parameters, and calculating the evaluation function using the returned model parameters.

Further, a term for preventing occurrence of bias due to use / non-use of equipment is added to the evaluation function.

[0008] In addition, a model determined from a theoretical value using elite preservation selection that always retains the individual with the highest fitness as it is in the next generation, including the individual created by the model parameters determined from the theoretical value, in the initial generation. This is to obtain better parameters than parameters.

An apparatus for automatically determining a number of model parameters for minimizing a predetermined evaluation function is provided by an apparatus for automatically determining model parameters, an evaluation function calculator for calculating the evaluation function, Encoding means for encoding in accordance with the absolute value level or the range theoretically possible, for converting into genetic information having a common upper and lower limit, for an individual which is a combination of the genetic information, Genetic processing means for performing genetic processing using an evaluation function to obtain a next-generation individual, and decoding means for decoding genetic information contained in the next-generation individual and returning to the corresponding model parameters And a model calculation means for performing a model calculation using the returned model parameters;
This problem is also solved by using a feature value extracting means for extracting a feature value for calculating an evaluation function for next-generation genetic processing from the model calculation result.

Further, the feature amount is a model error or a standard deviation.

Further, by providing storage means for storing the genetic information of the individual obtained by the genetic processing means, it is unnecessary to code the second and subsequent generations.

The following three points should be noted when determining model parameters.

Whether the model parameters to be determined are physically (theoretical) appropriate. Does the model calculation result using the determined model parameters well match the measured data? Which model parameters to change and to what extent.

In the above, human evaluations are various, and it is very difficult to apply ordinary optimization theory regardless of linear or non-linear.

On the other hand, a combination problem is a typical problem that is difficult to model, and a genetic algorithm is one of the solutions to such a combination problem. For example, JP-A-7
No. 219920 describes an application of a genetic algorithm to a truck allocation scheduling problem in the transportation industry, which is one of the combination problems.

This genetic algorithm is an optimization theory that simulates the evolution of living organisms. It is effective as a method for solving a combination problem, and can select an arbitrary numerical value as an evaluation function there. Therefore, this genetic algorithm is
If applicable to the determination of model parameters, the above problem can be solved.

On the other hand, it is necessary to make the upper and lower limits of the genes used in the genetic algorithm common among the genes. However, in general, since the physical (theoretical) upper and lower limits of each model parameter are different, this genetic algorithm cannot be used as it is for parameter determination of a control model. In the present invention, this problem is solved by changing the physical parameter conversion value per one quantum of gene between each gene.

[0018]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The embodiments of the present invention applied to a finishing mill temperature drop model in a hot rolling mill will be described in detail below with reference to the drawings.

The model of this embodiment is for calculating the distribution of the plate temperature T at each point of a finishing mill 10 having seven stands from a first stand F1 to a seventh stand F7 as shown in FIG. A finishing descaling device 12 and a finishing inlet thermometer 14 are provided on the input side of the finishing mill 10, and a finishing outlet thermometer 16 is provided on the outlet side of the finishing mill 10. In the finishing mill 10, not only the steel plate is water-cooled by the finishing descaling device 12, but also is injected from upper and lower independent cooling equipment 18 having water cooling nozzles provided on the entrance side and the exit side of each stand. Water cooling with a coolant such as water is performed. Further, air cooling is performed in regions other than the rolling region and the water cooling region immediately below each of the stands F1 to F7.

The heat conduction equation (model equation) used in this embodiment is as shown in the following equation.

(∂T / ∂t) = (k / Cpρ) · (∂ ² T / ∂x ² ) + (Q / Cpρ) (1) where T: plate temperature [K] t: air cooling / water cooling time [hr] x; thickness position [m] k: thermal conductivity [kcal / mhr ℃] Cp; specific heat [kcal / kg ℃] ρ; specific gravity [kg / m ^3] Q; generated heat [kcal / hrm ³ ]

As shown in FIG.
(K), the cooling water temperature is Tw (K), the surface temperature of the steel plate 8 is Tu (K), the back surface temperature is Tl (K), and the surface heat transfer amount of the steel plate 20 is Qu (kcal / hrm ² ). Assuming that the heat transfer amount on the back surface is Ql (kcal / hrm ² ), the heat transfer amount Qa on the front (back) surface of the steel sheet on the front surface or the back surface during air cooling is expressed by the following equation.

Qa = εσ (Ts ⁴ −Ta ⁴ ) + αa (Ts−Ta) (2)

Similarly, the water-cooled heat transfer amount Qw is expressed by the following equation.

Qw = εσ (Ts ⁴ −Tw ⁴ ) + αw (Ts−Tw) (3)

Similarly, the temperature change ΔT (° C.) during rolling is:
It is expressed by the following equation.

ΔT = ξ × (heat generated by friction) −κ × (heat released from roll) + η × (heat generated during processing) (4) Here, Ts: temperature of steel plate surface (back surface) [° C.] ε; emissivity σ; Boltzmann constant [kcal / m ² hr ° C ⁴ ] αa; Heat transfer coefficient during air cooling [kcal / m ² hr ° C] αw; Heat transfer coefficient during water cooling [kcal / m ² hr ° C] ξ; Friction heating efficiency κ; Heat correction coefficient η; Heat conversion ratio of machining work

Here, the amount of heat transfer is calculated separately for the front and back surfaces, and the temperature change during rolling can be common in the thickness direction.

Of the adjustment parameters in such a model, those used in the calculation at the time of air cooling include emissivity (common for upper and lower sides) and convection heat transfer coefficient for air cooling (upper and lower) set for each air cooling zone. is there. In addition, emissivity (upper and lower common), finish descaling water cooling heat transfer coefficient (up and down), strip coolant water cooling convection heat transfer coefficient (up and down) set for each water cooling zone are used for calculations during water cooling. , Roll coolant water cooling convection heat transfer coefficient (up and down). Further, as the ones used in the calculation at the time of rolling, there are the friction heat generation efficiency, the roll heat removal correction coefficient, and the heat conversion ratio of the processing work for each of the stands F1 to F7.

In the present embodiment, the present invention is applied to obtain an optimum value for a total of 23 heat transfer coefficients used in the calculation during water cooling, out of a large number of approximately 150 adjustment parameters as described above. Was. As a criterion, a parameter that minimizes the evaluation function J expressed by the following equation was set as an optimal parameter.

[0031]

(Equation 1)

Note that the first and second terms of the evaluation function J are added so that a large deviation does not occur due to the use / non-use of the cooling equipment. The third and fourth terms are used to reduce the model accuracy. This is the section to be evaluated.

An apparatus for carrying out this embodiment is shown in FIG.
As shown in FIG. 5, the evaluation function calculation unit 20 for calculating the evaluation function J, and each of the model parameters θ _{1 to} θ _m are coded according to their absolute value levels and theoretically possible ranges.
Gene information α ₁ to α having common upper and lower limits αmin and αmax
a coding unit 22 for converting alpha _m, with respect to an individual a combination of the genetic information alpha ₁ to? _m, the evaluation function J
And a genetic (GA) processing unit 24 for obtaining a next-generation individual by performing genetic processing using the same, and decoding for decoding the genetic information contained in the next-generation individual and returning it to the corresponding model parameter Conversion unit 26 and a model calculation unit 2 that performs a model calculation using the returned model parameters
8 and a feature value extraction unit 30 for extracting a feature value for calculating an evaluation function J for next-generation genetic processing from the model calculation result.

Hereinafter, the operation of the present embodiment will be described.

First, an outline of the genetic algorithm will be described with reference to FIG. In this genetic algorithm, for example, a large number of individuals (gene sequences; also referred to as chromosomes) 40 in the i-1 generation (individual group) are selected by random numbers to select one individual from the individual group. An individual with high fitness (an individual with a small evaluation function J) is selected based on the probability. This is a process of replacing a part of the selected one individual with a part of an individual selected separately. By performing “crossover” (a mother individual is a high fitness individual), “mutation” which is a process of changing genetic information with a mutation probability, and the like, for example, the same number as the i−1 generation The i-th generation individual 40 is obtained.

In the "selection", it is possible to adopt an elite preservation selection that always leaves the individual with the highest fitness as it is in the next generation.

Each model 40 has a model parameter
θ₁~ Θ_mGene information α corresponding to ₁~ Α_mPut on
ing. Unlike normal genetic information, model parameters
In the case of, the absolute value level and the theoretically possible range are
As shown on the right side of FIG. So search
Region center offset γ₁~ Γ_mAnd adjust the range
Conversion factor β for₁~ Β_mUsing, for example, the relationship
Gives the model parameter θ₁~ Θ_m, The common upper and lower limits
Genetic information α with values αmin and αmax₁~ Α_mConvert to
You.

Α ₁ = (θ ₁ −γ ₁ ) / β ₁ α ₂ = (θ ₂ −γ ₂ ) / β ₂ (6) α _m-1 = (θ _m-1 −γ _{m- 1} ) / β _m-1 α _m = (θ _m -γ _m ) / β _m

By performing such encoding,
Parameter adjustment of the model parameters by the genetic algorithm becomes possible.

It is to be noted that a new
Genetic information α₁~ Α_mIs obtained, for example, the following equation
This is decoded using the relationship of
TA θ ₁~ Θ_mReturn to

Θ ₁ = γ ₁ + β ₁ * α ₁ θ ₂ = γ ₂ + β ₂ * α ₂ (7) θ _m-1 = γ _m-1 + β _m-1 * α _m-1 θ _m = Γ _m + β _m * α _m

For the initial generation (first generation), genetic information can be created by generating random numbers or given in advance. If an individual is created from model parameters determined from theoretical values and the like in the initial generation, and the best individual is always saved by using elite preservation selection, a parameter value greater than or equal to the theoretical parameter can be always obtained.

Hereinafter, a specific processing procedure will be described with reference to FIG.

First, in step 100, an initial generation in a parameter space is created by using model parameters determined from, for example, theoretical values. Then step 102
Then, a model operation is performed using the initial generation, and step 1
In step 04, feature quantities such as the average and standard deviation of model errors are extracted. Next, the routine proceeds to step 106, where it is determined whether or not the calculation has been completed for all individuals of the generation (here, the initial generation). If the calculation of the individual of the generation remains, the process returns to step 102, and the model calculation and the feature amount extraction are repeated.

When the result of the determination in step 106 is positive, and the data operation has been completed for all individuals of the generation, the process proceeds to step 108, where an evaluation function J is calculated for each individual of the generation. Then, the process proceeds to a step 110, wherein the model parameter is set to θ ₁ by using, for example, the relationship of the above equation (6).
Encoding through? _M determined genetic information alpha ₁ to? _M and.
Next, the process proceeds to step 112, where a genetic (GA) process as shown in FIG. 4 is performed to create the next generation. Next, proceeding to step 114, the next-generation gene information obtained in step 112 is decoded using, for example, the relationship of equation (7) and returned to the model parameters. Then step 1
Proceeding to 16, it is determined whether or not genetic processing of a predetermined generation, for example, 15 generations, has been completed. If the result of the determination is negative, the process returns to step 102 and repeats the model calculation and subsequent steps. On the other hand, the determination result of step 116 is positive, and GA
When it is determined that the search has been completed, the processing is terminated.

In the second and subsequent generations, the encoding process can be omitted if the genetic information in the GA process that created the generation is stored.

In the above embodiment, the present invention is applied to the calculation of 23 heat transfer coefficients at the time of water cooling used in the finishing mill temperature drop model in a hot rolling mill. The present invention is not limited to this, and can be applied to calculation of other parameters of the finishing mill temperature drop model and determination of parameters of other models such as a deformation resistance model. The invention is not limited to the fields of rolling and steel.

[0048]

EXAMPLE For a 1500 coil centered on low carbon steel, the number of individuals (the number of sets of model parameters) is assumed to be 100 individuals.
Calculations were made for 15 generations. In evaluating the model parameters, the deviation between the actually measured value of the finishing thermometer 16 and the model calculation result calculated using the rolling performance was evaluated. Further, as shown in the first and second terms on the right side of the equation (5), this was added to the evaluation function J of the genetic algorithm so that no large deviation occurs due to use or non-use of each cooling facility.

FIG. 7 shows the transition of the average of the error and the standard deviation between the generations in this embodiment. It can be seen that the model parameters are optimized by the genetic algorithm.

FIG. 8 shows each cooling equipment 1 of the finishing mill 10.
8 shows a comparison of error averages when using (ON) / not using (OFF) No. 8, it can be seen that there is no large deviation due to the presence or absence of strip coolant injection from the nozzle of the cooling equipment 18. .

[0051]

According to the present invention, a parameter for minimizing an arbitrary numerical evaluation function within the range of the physical (theoretical) upper and lower limits of the model parameter to be determined,
It is possible to determine automatically and efficiently.

Therefore, it is possible to quickly and without human intervention to determine model parameters, which has conventionally been performed by a human over a long time and with a large load by trial and error.

[Brief description of the drawings]

FIG. 1 is a diagram showing a schematic configuration of a finishing mill to which the present invention is applied;

FIG. 2 is a plan view for explaining symbols of a finishing mill temperature drop model used in the embodiment of the present invention.

FIG. 3 is a block diagram showing the configuration of an automatic model parameter determination device according to the embodiment.

FIG. 4 is a diagram showing an outline of a genetic algorithm used in the embodiment.

FIG. 5 is a diagram showing the principle of encoding and decoding.

FIG. 6 is a flowchart showing an example of a processing procedure in the embodiment.

FIG. 7 is a diagram illustrating an example of transition between generations of an error average and a standard deviation for illustrating a state of optimization by a genetic algorithm in the embodiment.

FIG. 8 is a diagram showing an example of an error average when each cooling facility is used / not used to show that the evaluation function is reflected in the embodiment.

[Explanation of symbols]

8 Steel plate 10 Finishing mill 14 Finishing thermometer 16 Finishing thermometer 18 Cooling equipment 20 Evaluation function calculation unit J Evaluation function 22 Encoding unit 24 Genetic (GA) processing unit 26 Decoding unit 28 Model calculation unit 30 Feature extraction unit 40 Individual α _{1 to} α _m Gene information θ _{1 to} θ _m Model parameters

Claims (6)

[Claims] When deciding a large number of model parameters for minimizing a predetermined evaluation function, each model parameter is coded according to its absolute value level or a theoretically possible range, and a common upper and lower limit is determined. Is converted into genetic information having a value, and the individual that is a combination of the genetic information is subjected to genetic processing using the evaluation function to obtain a next-generation individual, and the genetic information contained in the next-generation individual is obtained. A method for automatically determining model parameters, comprising decoding and returning to corresponding model parameters, and calculating the evaluation function using the returned model parameters. 2. The method for automatically determining model parameters according to claim 1, wherein a term for preventing occurrence of bias due to use / non-use of equipment is added to said evaluation function. 3. The elite storage selection according to claim 1, wherein an individual having the highest fitness is always left in the next generation, including an individual created by a model parameter determined from a theoretical value. Method for automatically determining model parameters to be used. 4. An apparatus for automatically determining model parameters for minimizing a predetermined evaluation function and automatically determining a large number of model parameters, comprising: an evaluation function calculation unit for calculating the evaluation function; Coding means for coding parameters according to their absolute value levels and theoretically possible ranges and converting them into genetic information having common upper and lower limits; and an individual which is a combination of the genetic information. A genetic processing means for performing a genetic process using the evaluation function to obtain a next-generation individual; and a decoding device for decoding genetic information contained in the next-generation individual and returning to a corresponding model parameter. Means for performing a model operation using the returned model parameters; and calculating an evaluation function for next-generation genetic processing from the model operation result. Automatic determination device of the model parameters, characterized in that it includes a feature value extraction means for extracting a feature value of the eye. 5. An apparatus according to claim 4, wherein said characteristic amount is a model error or a standard deviation. 6. The apparatus according to claim 4, further comprising storage means for storing genetic information of the individual obtained by said genetic processing means.