JPH07121505A - Method for optimizing simulation model - Google Patents

Abstract

PURPOSE:To provide an optimizing method for constructing a simulation model capable of effectively simulating a practical processing process. CONSTITUTION:In the optimization of the simulation model 3 expressing the practical processing process 1 by an expression, a limited analytical function having a highly sensitive area capable of easily reflecting the weighted variation of a deviation between a predictive output obtained from the model 3 and an output obtained from the process 1 as an evaluation value as a deviation evaluating function for evaluating the deviation and the optimum value of each parameter or the like for the model 3 is recursively determined by the use of a generalized delta rule.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for optimizing a simulation model, such as a control model or a measurement model, which is represented by a mathematical expression for approximating physical phenomena in a field where it is necessary to simulate certain physical phenomena. Is.

[0002]

2. Description of the Related Art For large-scale processing processes (physical phenomena) that make up a steel plant, etc., when the processing conditions are set again so that desired characteristics can be obtained for each of a wide variety of products, When the optimum processing conditions are sequentially set based on the result obtained by operating the target processing process (output information obtained from the actual processing process and the actual physical quantity obtained from the sensor, etc.) , Enormous cost is required.

Therefore, conventionally, a simulation model (in particular, a simulation model in which process characteristics are expressed by a mathematical expression) that approximates the above-described processing process with a mathematical expression is prepared in advance so that desired characteristics (output result) can be obtained from this simulation model. It was general that the treatment conditions were sequentially changed, and after the treatment conditions of the treatment process were set when the desired characteristics were obtained, the treatment process was actually operated.

Therefore, it is important that the above simulation model closely approximates the actual treatment process. In FIG. 9, the actual output result of the treatment process 1 actually operating (obtained from the treated material) is shown. 1 shows a structure of a conventional signal processing apparatus A for realizing an optimization method of a simulation model for resetting to an optimum processing condition so that various physical quantities given) have desired characteristics.

In this figure, a conventional signal processing device A
Compares the simulation model 3 represented so as to approximate the actual process 1 to be processed with a mathematical expression with the output (predicted output) from the simulation model 3 and the desired characteristic 4 prepared in advance. The error evaluation means 2 is configured to sequentially instruct the simulation model 3 to change the processing conditions so as to calculate an error and obtain a value approximate to the desired characteristic 4.

That is, in the conventional signal processing apparatus A, as information of the material actually supplied to the processing process 1, a plurality of parameters Z _j which are various physical quantities obtained by a sensor (not shown) and the processing process. The processing condition parameter is input to the simulation model 3, and the predicted value is obtained from the simulation model 3 as the predicted output X _j of the processing process 1.

In parallel with the operation of obtaining the predicted output X _j from the simulation model 3, the error evaluation means 2 successively finds the error between the predicted output X _j of the simulation model 3 and the desired characteristic 4, and this error falls within a predetermined range. If it is not within the range, the simulation model 3 is newly instructed to change the processing condition, and the processing condition is set so that the predicted output X _j of the simulation model 3 approaches the desired characteristic 4.

When the error evaluation means 2 determines that the error between the predicted output X _j of the simulation model 3 and the desired characteristic 4 is within the allowable range, the processing condition already instructed to the simulation model 3 is determined. Is set as the optimum processing condition, and an instruction for setting the optimum processing condition is given to the processing process 1 which is the actual simulation target.

However, the conventional signal processing apparatus A described above is used.
In particular, the problem is that the accuracy and reliability of the simulation performed by the signal processing apparatus A largely depend on the degree of perfection of the simulation model 3.
That is, the signal processing apparatus A performs the calculation depending on the extent to which the simulation model 3 simulating the operation of the processing process 1 approximates the characteristics of the processing process 1 (is represented by a sufficiently approximated mathematical expression). This means that the accuracy and reliability of the simulation are determined.

Therefore, in the past, from the predicted output X _j obtained from the simulation model 3 in the conventional signal processing apparatus A and various physical quantities (T _j ) of the actual processed material under a predetermined condition, An optimum value is calculated by using an optimization means 5 such as regression, and the simulation model 3 in the signal processing apparatus A is calculated according to the optimum value.
Tuning was performed manually to approximate the process process 1 to the actual process process 1.

The optimization method carried out by the optimization means 5 for obtaining the optimum value as described above will be described below.

First, in the linear regression method, when the measured quantities X and Y have a linear function relationship, n sets of measured values are x _i ,
As y _i (i = 1, 2, ..., N), y (x _i ) = a + b · x _i . When the variance of x _{i in} the above equation is small enough to be ignored, and y _i follows a normal distribution, and variances σ ² are all equal, the evaluation function of the above linear function is

[0013]

[Equation 1]

In order to obtain the coefficients a and b that minimize the evaluation function χ ² ,

[0015]

[Equation 2]

Optimization is performed by solving the simultaneous equations of. Therefore, we rewrite this system of equations as follows,

[0017]

[Equation 3]

Optimal solutions a and b are obtained by using normal equations.

[0019]

[Equation 4]

However,

[0021]

[Equation 5]

It is assumed that

Next, the curve regression method will be described. This method uses n sets of measurement values x _i , y _i (i = 1, 2, ...,
When n) has the following quadratic function relationship, Y = a + b · X + c · X ²

[0024]

[Equation 6]

[0025] defined, the coefficients a for the evaluation function chi ² minimizes, b, for obtaining the c, following partial differential equation ^{∂χ 2 / ∂a = 0, ∂χ} 2 / ∂b = 0, ∂χ ² / ∂c =
From 0, the following simultaneous equations are obtained.

[0026]

[Equation 7]

Then, the optimum solution is obtained by obtaining the coefficients a, b, and c for this simultaneous equation.

Next, a case will be described in which the following polynomials are optimized using the least squares method.

When the variable Y is represented by the P-order equation (the following equation) of the variable X, Y = a + b.X + ... k.X ^P The variance of this variable X is so small that it can be ignored, and the variable Y is the variance σ ² , Where n is a constant normal distribution, and n sets of measurement values are x _i , y _i (i = 1, 2, ..., N), each coefficient a, b ,.

[0030]

[Equation 8]

The solution is obtained, and each of these coefficients becomes the optimum solution.

Next, a case will be described in which the following multidimensional linear equation is optimized using the least squares method.

The quantities to be obtained are x, y, ..., T, respectively,
When n sets of measured values are q _i (i = 1, 2, ..., N), the multidimensional linear equation for each coefficient a _i , b _i , ..., K _i is a _i · x + b _i · For y + ... + k _i · t = q _i , each solution (x,
y, ..., t) is obtained as an optimal solution.

[0034]

[Equation 9]

However, w _i is a weight, and when each solution has a normal distribution, this weight w _i is w _i = 1 / σ _i ² .

The above optimization method is disclosed in, for example, Akimichi Takemura, "Modern Mathematical Statistics," (Sobunsha Modern Economics Selection).

[0037]

Problems to be Solved by the Invention For example, FIG.
As shown in (4), as a function that best describes the relationship between x and y, in order to minimize the error evaluation function E represented by the error mean square shown in Expression 10, each of the functions y = g (x) Consider the case of determining parameters.

[0038]

[Equation 10]

The subscript j in the equation indicates that it is the j-th data.

In such a conventional multiple regression method, since the square of the error is used as the evaluation function, most of the predicted output data obtained from the simulation model have a small error, and only a small number of the data. If has a large error, the data with this large error would be overestimated.

That is, 100 where the absolute value of the error is 1.
The data (1 ² × 100 = 100) and the one data (10 ² × 1 = 100) having an absolute error value of 10 have the same contribution to the error evaluation function. Therefore, FIG.
As shown in 0 (b), even if most of the data (indicated by x in the figure) is within the range of the error ± 1 of the function y = g (x) shown by the solid line, for example, the error − If there are 10 data (indicated by ▲ in the figure), a function that minimizes the evaluation function (as indicated by a broken line (y = g ′ (x)) in the figure due to the influence of the data having the large error ( Specifically, the function g ′) that cannot be said to properly represent the relationship between the predicted output from the simulation model and the output from the actual processing process becomes a function that gives a relationship between x and y. However, there is a problem that the optimum error evaluation cannot be performed.

The present invention has been made to solve the above problems, and even if there is data having a large deviation in the predicted output data obtained from the simulation model, these large deviations are present. For building a simulation model that allows an evaluation to find the optimal function that describes the relationship between the majority of the predicted output data, without being affected by the data with The aim is to get an optimization method.

[0043]

A method for optimizing a simulation model according to the present invention is a model for simulating the behavior of an actual processing process under various processing conditions, and the simulation expressing the processing process by a mathematical expression. A model, for example, a model that approximates the rolling process in a steel plant, for predicting the behavior of the actual rolling process from the predicted output for the actual physical quantity obtained from the steel material given to the rolling process under predetermined processing conditions We are aiming for optimization technology for simulation models.

In addition to the above rolling process, the actual treatment process in the present invention corresponds to, for example, a vapor phase growth process of a semiconductor, an alloying process of a surface-treated steel plate, an oxidation process of a plated steel plate and the like. Further, as the actual physical quantity obtained from this actual processing process, in the case of the rolling process, for example, the strip width in hot rolling,
The plate thickness and crank, or the plate thickness and crown in cold rolling are applicable.

Then, the above-mentioned predicted output and the actual processed data when the simulation model is optimized (the optimum values of the parameters of the simulation model are determined so that the simulation model closely approximates the actual processing process) Regarding the deviation evaluation from the physical quantity obtained from the material, the following bounded analytic function is applied as the deviation evaluation function used in the optimization method.

That is, the deviation evaluation function is as follows: (1) f (0) = 0 (2) x> 0, f (x) monotonically increases in a narrow sense. (3) f is an even function, that is, f (x ) = F (−x) is satisfied (4) f is defined as a bounded analytic function satisfying the above conditions (having a horizontal asymptote).

The deviation in this specification is a concept including an error or an error variance between the predicted output and a physical quantity obtained from an actual processed material.

The parameters of this bounded analytic function are
Predicted output of the simulation model (vector Y _j ) and output of the actual processing process (vector T _j )
Each

[0049]

[Equation 11]

[0050]

[Equation 12]

Then (note that the subscript j indicates the jth data, and each data may be a scalar), the number of dimensions n of the prediction output of these simulation models and the output of the actual processing process is n. By defining a positive definite symmetric matrix A having its matrix size as, the variation is given as the weighted deviation as shown below.

[0052]

[Equation 13]

Alternatively,

[0054]

[Equation 14]

In the equation, E _{f, A} is a deviation evaluation function determined by defining the bounded analytic function f and the positive definite symmetric matrix A satisfying the above conditions. In particular, the prediction output of the simulation model and the output of the actual processing process may each be a scalar, and in this case, the deviation evaluation function E _{f, A} is E _{f, A} (Y _j , T _j ) = f (A (Y _j −T _j )) or

[0056]

[Equation 15]

Is given by The positive definite symmetric matrix A at this time is a ² (a> 0).

Furthermore, in the optimization method of the simulation model according to the present invention, when the simulation model approximating the processing process is optimized, the above-mentioned simulation model should be set so as to minimize (or maximize) the deviation evaluation function defined above. The optimum value of each parameter (or function form) in (1) is recursively determined using, for example, a generalized delta rule, and is specifically performed as follows.

That is, the output vector from the actual processing process (the vector T _j indicates the j-th vector data) and the predicted output vector of the simulation model (the vector X _j indicates the j-th vector data). The evaluation function E _{f, A} having the element is defined as in the above-described Expression 13 or Expression 14, and a positive definite symmetric matrix A having the same matrix size as the number of dimensions of each vector data is defined. Then, for example, the generalized delta rule is used to recursively find the optimum value of each parameter a _i of the simulation model that minimizes the deviation evaluation function E _{f, A.}
This is the following differential equation: da _i / dt = −η∂E _{f, A} / ∂a _i where η is a learning coefficient (or step size) for determining the convergence speed.

The amount of change is calculated from each of the parameters and each parameter a _i of the current simulation model is calculated as follows.
(T) and the new parameter a _i (t +
Δt) is determined and a _i (t + Δt) = a _i (t) −η∂E _{f, A} / ∂a _i These series of operations are performed until the deviation evaluation function E _{f, A} becomes minimum (or maximum). It is decided by repeating.

[0061]

The optimization method of the simulation model according to the present invention defines a bounded analytic function satisfying the above-mentioned conditions as a deviation evaluation function, and as shown in FIG. In the high-sensitivity region of this bounded analytic function, the absolute value of this deviation is greatly reflected as the evaluation value of the evaluation function, while in the section where the absolute value of the deviation is large (regions other than the high-sensitivity region), The absolute value has the property that it is difficult to reflect it as the evaluation value of the evaluation function. In FIG. 1, the horizontal axis represents the deviation between the predicted output of the simulation model and the output of the actual processing process (indicated by ERR in the figure), and the vertical axis represents the bounded analytic function defined as the deviation evaluation function E _{f, A.} It is a value.

Therefore, when each parameter of the simulation model is optimized so that the deviation evaluation function defined by the bounded analytic function as shown in FIG. 1 is minimized, data with large deviation is given to the evaluation value. Since the influence does not exceed a certain value, a proper target evaluation can be performed on the majority of the predicted output data without being influenced by the small number of outliers (data with large deviation).

Further, the deviation evaluation function is defined as a bounded analytic function for the variation weighted for each deviation (this bounded analytic function is a function satisfying the above-mentioned four conditions). By changing the positive definite symmetric matrix A defined in, the high sensitivity region of the deviation evaluation function can be freely set.

As a method of constructing a function without being affected by data with a large deviation (a method of determining the optimum value of each parameter that minimizes the deviation evaluation function), the deviation of the deviation before the optimization is performed. A method of excluding large data may be considered. However, this elimination method is shown in FIG.
As shown in, when the originally desired function is y = g ′ (x), the function y = g ″ affected by the data with large deviation
Although it is effective as a means for correcting (x), there is a risk that it cannot be applied at all when the originally desired function is y = g (x).

The deviation evaluation function in the present invention is defined as a bounded analytic function that does not make the degree of influence of data with large deviations a certain value or more, and the high sensitivity region of this deviation evaluation function can be continuously changed. In addition, since the optimum value of each parameter of the simulation model is recursively determined, even one of the data that is out of the majority of the predicted output data should be in the high sensitivity region of this deviation evaluation function. For example, it is possible to follow these deviated data (the situation is shown in FIG. 2B), and it becomes possible to construct an optimal simulation model that closely approximates the actual processing process.

[0066]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to FIGS. In the figure, the same parts are designated by the same reference numerals and the description thereof will be omitted.

FIG. 3 is a diagram showing an entire structure including a signal processing device B for realizing the simulation model optimization method according to the present invention. In particular, this signal processing device B is
A simulation model 3 represented by a mathematical expression for approximating the treatment process 1 that is actually operating, and an optimization means 6 for tuning the simulation model 3 by approximating the simulation process 3 by modifying each parameter. And the predicted output Y _j of the simulation model 3 tuned by the optimizing means 6 and the desired characteristic 4
If the deviation is not within the allowable range, the simulation model 3 is instructed to change the processing conditions.
If the deviation is within the allowable range, it is composed of deviation evaluation means 20 for setting the actual processing process 1 to the optimum processing condition.

The simulation model optimizing method according to the present invention can also be used for optimizing the simulation model 3 which is regularly tuned manually by hand as in the conventional method. In particular, in this embodiment, the simulation model 3 is optimized. The structure is not limited. Further, in this specification, the deviation is a concept including an error or an error variance between the predicted output and a physical quantity obtained from an actual processed material.

In the signal processing apparatus B, a plurality of parameters Z _j (vector data, which are various measured values obtained by a sensor (not shown) or the like, are used as the information of the material actually supplied to the processing process 1. Or a scalar) may be input to the simulation model 3 tuned by the optimizing means 6 in advance, and the predicted output Y _j (Y _j = g (Zj) of the processing process 1 described above may be input.
The output of the simulation model 3 is obtained as ( _j may be vector data or a scalar).

On the other hand, in parallel with the operation for obtaining the predicted output Y _j obtained from this simulation model 3, the deviation evaluation means 20 successively finds the deviation between the predicted output Y _j of this simulation model 3 and the desired characteristic 4, and this If the deviation is not within the predetermined range, the simulation model 3 is newly instructed to change the processing condition, and the processing condition is set so that the predicted output Y _j of the simulation model 3 approaches the desired characteristic 4. .

When the deviation evaluating means 20 determines that the deviation between the predicted output Y _j of the simulation model 3 and the desired characteristic 4 is within the allowable range, the processing condition of the adaptive model 6 is set to the optimum processing condition. As a result, the processing process 1 which is the actual simulation target is instructed to set the processing conditions.

Next, although the structure of the simulation model 3 is not particularly limited, in this embodiment, as shown in FIG.
A case will be described in which a Taylor series model that represents an arbitrary function as shown in FIG.

FIG. 4 is a diagram showing the configuration of the simulation model 3 approximating (representing by a mathematical expression) the actual processing process 1, and the sensor (as the information of the material actually supplied to the processing process 1) A constant c, which is the radius of convergence, is added (negative) to a plurality of parameters Z _j that are various measured values obtained by (not shown) or the like (these parameters Z _j may be vector data or a scalar). , And this constant may be zero) to calculate one or more power-law terms, and a pre-defined power-factor group a _{i corresponding} to each power-law term is calculated. The prediction output Y _j is obtained by adding all the multiplication results obtained by multiplying the respective power terms.

In particular, this simulation model 3 is a model g in which an arbitrary function is represented by Taylor series as follows.
(Z _j ) and

[0075]

[Equation 16]

The optimizing means 6 uses the actual processing process 1 described above.
By determining the optimum value of each constant c and the power factor group a _i based on the output (actual value T _j ), the predicted output (Y _j = g (Z _j )) of the simulation model 3 is obtained as a simulation model. The optimization is performed so that the deviation from the actual output of the processing process 1 is minimized.

On the other hand, the automatic tuning operation of the simulation model 3 by the optimizing means 6 includes the predicted output Y _j obtained from the simulation model 3 and the processing process 1.
A deviation evaluation function with respect to the output T _j obtained from the above is defined in advance (note that these data Y _j and T _j may be vector data or scalar), and this deviation evaluation function is generally minimized. The tuning of the simulation model 3 is automatically performed by sequentially determining the optimum values of the constants c and the power factor group a _i of the simulation model 3 according to the generalized delta rule.

That is, in the optimizing means 6, as a deviation evaluation function in advance, (1) f (0) = 0 (2) x> 0, f (x) monotonically increases in a narrow sense. (3) f is an even function. That is, f (x) = f (−x) is satisfied (4) f is bounded (has a horizontal asymptote) A bounded analytic function that satisfies the above conditions is defined (FIG. 1 is
Shows the general shape of this bounded analytic function).

The parameters of this bounded analytic function are
Prediction output of the above simulation model (vector Y _j
= G (Z _j )) and the output (vector T _j ) of the actual processing process, respectively.

[0080]

[Equation 17]

[0081]

[Equation 18]

Then (note that the subscript j indicates the jth data, and each data may be a scalar), the dimensions of the prediction output of these simulation models 3 and the output of the actual processing process 1 By defining a positive definite symmetric matrix A having the number n as its matrix size, it is given as a variation of each deviation weighted as shown below.

[0083]

[Formula 19]

Alternatively,

[0085]

[Equation 20]

In the equation, E _{f, A} represents the deviation evaluation function determined by defining the bounded analytic function f and the positive definite symmetric matrix A satisfying the above conditions.

FIG. 5 is a diagram showing the configuration of the deviation evaluation function calculating means 7 (included in the optimum chemical means 6) for obtaining the evaluation value of the deviation evaluation function E _{f, A} defined as described above. And an adder 7 that adds (negatively adds) the predicted output of the simulation model 3 (vector Y _j ) and the output of the actual processing process 1 (vector T _j ) for each component.
a, a positive definite symmetric matrix 7b defined in advance to adder 7
The matrix calculator 7c for weighting the variation of the deviation output from a, the square root calculator 7d for taking the square root of the weighted deviation variation output from the matrix calculator 7c, and the deviation output from this square root calculator 7d With respect to the fluctuation, the deviation evaluation value for the weighted deviation fluctuation is obtained by configuring the function calculation unit 7e that outputs the evaluation value of the deviation evaluation function E _{f, A} defined in advance.

Specifically, the bounded analytic function f (x) satisfying the above-mentioned conditions as the deviation evaluation function is

[0089]

[Equation 21]

It is defined as

At this time, the number of dimensions n of the predicted output Y _j of the simulation model 3 and the output T _j of the processing process 1 is 1
, If it is a scalar, then the positive definite symmetric matrix A
Is defined as a ² (a> 0), the deviation evaluation function E _{f, A} is defined as shown below from the above-mentioned mathematical expression 20, for example.

[0092]

[Equation 22]

When the number of dimensions n of the predicted output Y _j of the simulation model 3 and the output T _j of the processing process 1 is 2 (in the case of vector data), the positive definite symmetric matrix A
Is defined as follows,

[0094]

[Equation 23]

As shown in FIG. 6, the high-sensitivity region of the bounded analytic function f defined as the deviation evaluation function can be elliptical. In the figure, ERR1 and ERR2 represent the respective components of the vector data representing the deviation, and the deviation evaluation function is defined by, for example, the above mathematical expression 20.

Further, in the optimization means 6, the optimum values of the respective parameters a _i and c of the simulation model 3 for minimizing the deviation evaluation function E _{f, A} defined as above are
Differential equation using the generalized delta rule da _i / dt = −η∂E _{f, A} / ∂a _i dc / dt = −η∂E _{f, A} / ∂c where η is for determining the convergence speed It is a learning coefficient (also called a step size).

The respective change amounts are calculated from the above, and added to the constant c (t) at the present time and each power coefficient group a _i (t) as follows to obtain a new constant c (t + Δt) and each power coefficient. The group a _i (t + Δt) is determined as follows: a _i (t + Δt) = a _i (t) −η∂E _{f, A} / ∂a _i c (t + Δt) = c (t) −η∂E _{f , A} / ∂c By repeating this series of operations until the deviation evaluation function E _{f, A} defined as described above is minimized, the simulation model 3 can be further approximated to the process 1.

Next, as a concrete example, the actual treatment process 1 is used as an actual rolling process, and the optimization of the simulation model 6 in which this rolling process is expressed by a mathematical expression will be described.

FIG. 7 is a diagram for explaining a rolling situation in a rolling process which is a simulation target by showing a cross section of a steel plate which is a material.

FIG. 10A shows rolling from the left and right direction of the plate width WI (direction from the edge of the plate toward the center) (referred to as edging rolling), and by rolling from the left and right, FIG. ) Obtain a cross section as shown in FIG. From this figure,
Since it is rolled from the left-right direction, the edge part is crushed so as to protrude in the thickness HI direction (the part where the white background part protrudes in the figure), and the closer to the center, the less the effect of edging rolling. .

Then, in the horizontal direction (direction from the center of the plate to the edge) with respect to the edging-rolled steel plate shown in FIG.
When it is rolled (referred to as horizontal rolling), the portion protruding in the thickness HI direction shown in FIG. 7B is also horizontally rolled by the horizontal rolling so as to have a uniform thickness HO (FIG. )).

Here, considering the contribution of each part rolled in the horizontal direction by the horizontal rolling (the process from FIG. 11B to FIG. 11C), the horizontal rolling results in the same figure (b). The white background portion (referred to as a dog bone) in FIG. 4A) contributes to the white background portion in FIG. 7C, while the white background portion in FIG.
The shaded portions in () can be considered as models that contribute to the shaded portions in FIG.

The model formula generated based on the above rolling process, that is, the predicted output WO of the simulation model 3 is shown below.

First, as input parameters (information obtained from treatment process and material): WE: strip width after edger rolling WI: strip width before edger rolling HO: strip thickness after horizontal rolling HI: strip thickness before horizontal rolling RE: edger roll radius RR: When the horizontal roll radius is given, the final output WO (predicted output) of this simulation model 3 is WO = WH + WD + WE where WH = ((HI / HO) ^{g (α)} −1) WE WD = g (β) · (WI-WE) At this time, the function g shown in the equation is a function that expands the arbitrary function shown in the above equation 16 into a Taylor series, and the respective parameters α and β are

[0105]

[Equation 24]

Here, LD = {RR · (HI-HO)}
^1/2

[0107]

[Equation 25]

As an output of the treatment process 1 (steel rolling process), it is assumed that actual values are obtained from the treated material by a sensor or the like, and a deviation evaluation function E _{f from the} actual value to the predicted output of the simulation model 3 is obtained. _{, A} , the differential equation da _i / dt = −η∂E _{f, A} / ∂a _i dc / dt = −η∂E _{f, A} / ∂c where η is a learning coefficient () for determining the convergence speed. It is also called a step size).

By solving for each of the change amounts, a new constant c (t + Δ is obtained by adding it to the current constant c (t) and each power factor group a _i (t) as follows.
t) and each power factor group a _i (t + Δt) are determined as follows: a _i (t + Δt) = a _i (t) −η∂E _{f, A} / ∂a _i c (t + Δt) = c ( t) −η∂E _{f, A} / ∂c By repeating these series of operations until the deviation evaluation function E _{f, A} defined as described above is minimized, the actual rolling process including the simulation model 3 is approximated. You can build a model that works.

Further, the above equations 19 and 20 are shown as the deviation evaluation function. The steepest descent method of the equation 20 is shown in FIG.
As shown in (a), the optimum solution is directly reached in the course of learning, whereas the relaxation method of Expression 19 sequentially obtains the optimum solution for each given data as shown in FIG. 8 (b). There is a feature called. Therefore, considering the effect of learning, it is necessary to use the steepest descent method (Equation 20), and to learn each data (to realize online learning) the relaxation method (Equation 19). , Can be used properly according to the purpose.

[0111]

As described above, according to the present invention, as a deviation evaluation function for optimizing a simulation model approximating an actual processing process, as shown in FIG. Small area (high sensitivity area)
In this case, while the absolute value of the deviation is greatly reflected in the evaluation value of the evaluation function, in the section where the absolute value of the deviation is large (areas other than the high sensitivity area), the absolute value of the deviation is reflected in the evaluation value of the evaluation function. Since we have defined a bounded analytic function that is difficult to do, the influence of data with large deviation on the evaluation value does not exceed a certain value, and it is large without being affected by these few outliers (data with large deviation). Appropriate evaluation can be performed for a large number of predicted output data (a simulation model that closely approximates the actual processing process can be constructed)
There is an effect.

Further, the deviation evaluation function in the present invention is a bounded analytic function having a deviation variation pre-weighted by the positive definite symmetric matrix A as a parameter (this bounded analytic function is a function satisfying the above-mentioned four conditions. ), By changing the positive definite symmetric matrix A defined for this weighting, it is possible to continuously and freely set the high sensitivity region of the deviation evaluation function.

Further, the deviation evaluation function in the present invention is defined as a bounded analytic function that does not make the degree of influence of data with a large deviation larger than a certain value, and the high sensitivity region of this deviation evaluation function is continuously changed. Since it is possible to recursively determine the optimum value of each parameter of the equation that represents the simulation model,
If even one piece of data that deviates from the majority of the predicted output data enters the high-sensitivity region of this deviation evaluation function, it is possible to follow the data that deviate, and a simulation model that approximates the actual processing process favorably. The effect is that optimization can be performed.

[0114]

[Brief description of drawings]

FIG. 1 is a diagram showing a general form of a bounded analytic function defined in advance as a deviation evaluation function in a simulation model optimization method according to the present invention.

FIG. 2 is a diagram for explaining the operation of the simulation model optimization method according to the present invention.

FIG. 3 is a diagram showing a configuration of an entire plant including a signal processing device that realizes a simulation model optimizing method according to the present invention.

FIG. 4 is a diagram showing a configuration of a simulation model and an optimizing means to which the optimizing method is applied in the signal processing device for realizing the optimizing method of the simulation model according to the present invention.

FIG. 5 is a diagram showing a configuration of deviation evaluation function calculation means for outputting an evaluation value for each deviation in the signal processing device for realizing the simulation model optimization method according to the present invention.

FIG. 6 is a diagram showing an example of a high-sensitivity region of a deviation evaluation function when a predetermined positive definite symmetric matrix having a dimension of 2 is defined.

FIG. 7 is a diagram showing, for example, each processing step of a rolling process as an actual processing process that is a simulation target of the simulation model in the present invention.

FIG. 8 is a diagram showing a case where the steepest descent method and a relaxation method are used as the optimization method in the simulation model optimization method according to the present invention.

FIG. 9 is a diagram showing a configuration of a signal processing apparatus for realizing a conventional simulation model optimization method.

FIG. 10 is a diagram for explaining a problem in a conventional simulation model optimization method.

[Explanation of symbols]

1 ... Processing process, 20 ... Deviation evaluation means, 3 ... Simulation model, 4 ... Predetermined characteristic, 6 ... Optimization means, 7 ...
Deviation evaluation function calculation means.

Claims (3)

[Claims] 1. A model for simulating the behavior of an actual treatment process under various treatment conditions, which is given under predetermined treatment conditions in a simulation model optimization method in which the treatment process is expressed by a mathematical expression. As a deviation evaluation function for evaluating the deviation between the predicted output obtained from the simulation model and the output obtained from the processing process with respect to the input information, there is a high-sensitivity region in which weighted variation of the deviation is easily reflected as an evaluation value. A method for optimizing a simulation model, which comprises defining a bounded analytic function and determining an optimum value of each parameter or function form of the simulation model that maximizes or minimizes the deviation evaluation function. 2. A model for simulating the behavior of a rolling process under various processing conditions, which is applied to the rolling process under predetermined processing conditions in an optimization method of a simulation model in which the rolling process is expressed by a mathematical formula. For the actual physical quantity obtained from the steel material, as a deviation evaluation function to evaluate the deviation between the predicted output from the simulation model and the actual physical quantity obtained from the processed steel material that has been rolled by the rolling process, Define a bounded analytic function having a high sensitivity region in which the weighted variation of the deviation is easily reflected as an evaluation value, and determine the optimum value of each parameter or function form of the simulation model that maximizes or minimizes the deviation evaluation function. A method for optimizing a simulation model characterized by: 3. The high-sensitivity region of the bounded analytic function is defined by changing a positive definite symmetric matrix defined to weight evaluation targets of the prediction output obtained from the simulation model and the actual output information. The optimization method of the simulation model according to claim 1 or 2, wherein the area is a resettable area.