JPH06337853A - Signal processing method and its device - Google Patents

Abstract

PURPOSE:To automatize tuning work and to obtain a universal optimizing result by judging whether or not output obtained from a physical model is to be used for optimizing prior to optimizing and selecting data to be used. CONSTITUTION:In a signal processor B, a selection means 6 judges whether the output Xi of the physical model is to be used for optimizing the parameter of the physical model for making it approximate to the output Ti of a processing process. Namely, the selection means 6 calculates the function value of a probability density function which is previously defined as an evaluation function judging whether or not the output Xi from the physical model is to be used for optimizing and cimpares the function value with a prescribed threshold. An optimizing means 7 decides a contribution degree for optimizing with respect to a data group adopted in the selection means 6, calculates the update quantity of the respective parameters, updates a parameter value before update by updated quantity corrected in accordance with the calculated contribution degree and calculates the new parameter value.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention automatically applies a simulation model to a physical model expressing a certain physical phenomenon by a mathematical expression, such as a control model and a measurement model. And a device therefor.

[0002]

2. Description of the Related Art As a certain physical phenomenon, for example, in the case of resetting each processing condition so that desired characteristics can be obtained for each of a variety of products for a large-scale processing process constituting a steel plant or the like. If the optimum processing conditions are sequentially set based on the result (output information) obtained by actually operating the target processing process, enormous cost is required.

Therefore, conventionally, a physical model (in particular, a physical model in which process characteristics are expressed by mathematical formulas) expressing the above-mentioned processing process in advance is prepared, and an output result having desired characteristics is obtained for this physical model. It is a general practice to sequentially change the treatment conditions as described above, set the treatment conditions of the treatment process when the desired characteristics are obtained, and then actually operate the treatment process.

FIG. 9 shows a conventional method for setting the optimum processing conditions so that the actual output results of the actually operating processing process 1 (various measured values of the processed material) have desired characteristics. It is a figure which shows the structure of the signal processing apparatus A which implement | achieves the signal processing method of.

In this figure, a conventional signal processing device A
Compares the physical model 3 represented so as to approximate the actual target process 1 with a mathematical expression, and the output (predicted output) from the physical model 3 and the desired characteristic 4 prepared in advance. The error evaluation means 2 is configured to sequentially instruct the physical 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, a plurality of parameters Z _j , which are various measured values obtained by a sensor (not shown) or the like, are physically used as information on the material actually supplied to the processing process 1. It is input to the model 3 and its predicted value is obtained from the physical model 3 as the predicted output X _j of the processing process 1.

In parallel with the operation for obtaining the predicted output X _j from the physical model 3, the error evaluation means 2 successively finds the error between the predicted output X _j of the physical model 3 and the desired characteristic 4, and this error is within a predetermined range. If it is not within the range, the physical 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 physical 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 physical model 3 and the desired characteristic 4 is within the allowable range, the processing condition already instructed to the physical 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 depends on the physical model 3.
It depends on the degree of perfection. That is, the signal processing apparatus A is determined by how much the physical 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 to be performed are determined.

Therefore, conventionally, from the predicted output X _j obtained from the physical model 3 in the conventional signal processing apparatus A and the various measured values (T _j ) of the actual processed material at regular intervals,
The optimum value is calculated using the optimization means 5 such as multiple regression, and the physical model 3 in the signal processing apparatus A is manually tuned according to the optimum value to approximate the actual processing 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]

As described above, the conventional signal processing method and apparatus therefor perform the tuning of the physical model in the signal processing apparatus that is periodically performed (to obtain an appropriate output that can be used as a prediction output, (Reapproximating the physical model to the processing process) has been performed by re-setting each processing condition with the calculated optimum solution by the optimization means using a method such as multiple regression in an offline state.

Therefore, in the above tuning method, different solutions are obtained depending on the person who adjusts, or even if the same person adjusts at different times, a universal optimal solution is uniquely determined. However, there is a problem that it is difficult to prove that the obtained result is the optimum condition.

The optimizing means for optimizing the physical model (optimizing each parameter for approximating the output of the physical model to the output of the processing process) is widely used as a general-purpose method. However, the conventional signal processing method and its apparatus use all the outputs obtained from the physical model for the optimization without judging whether or not the data is used for the optimization of each parameter in the physical model. Was.

Therefore, as shown below, (1) When there is data having an erroneous value for some reason, if optimization is performed using a data group including this data, the optimization When the result is worse than the condition before optimization (2) If there is data that has an incorrect value for some reason, if optimization is performed using the data group containing this data, the optimum value will be obtained. It may not converge, or may have an adverse effect such as poor convergence efficiency.

Further, since there is no criterion for determining how important the data used for optimization should contribute to this optimization, all optimization is performed with the same contribution. In addition to the above-mentioned situations (1) and (2), there is a problem in that the conditions before optimization are not improved so much.

The present invention has been made in order to solve the above problems. As a physical phenomenon, for example, the optimization of a physical model in which an actual processing process is represented by a mathematical formula is conventionally relied on manually for tuning work. It is an object of the present invention to provide a signal processing method and an apparatus thereof that automates the above and obtain a universal optimization result.

[0043]

The signal processing method and the apparatus therefor according to the present invention include:
For example, when the output of the physical model that represents the actual processing process by a mathematical expression is further optimized in order to approximate the output of this processing process for each parameter in the physical model, it is obtained from the physical model prior to this optimization. It is characterized by determining whether or not the output to be used is data to be used for optimization and selecting data to be used for optimization.

In the signal processing method according to the present invention, in the first step, with respect to the output from the physical model, it is determined whether or not the output is data to be used for optimization. This is a function value of a probability density function defined in advance as an evaluation function for judging whether or not the output is data to be used for optimization, with respect to the output from the physical model, and this function value and a predetermined value. The feature is that it is performed by comparing with a threshold value.

Specifically, the above-mentioned first step is performed by the selecting means in the signal processing apparatus according to the present invention. First, the data value input in the past is x _i (i = 1,2,
, N), and the probability density function predefined as the evaluation function

[0046]

[Equation 10]

It is assumed that

At this time, x in the equation is output data from the physical model to be input in the future, m is the average value of the data values input in the past, σ ² is the variance thereof, and the average value m is, for example, of the normal distribution. As the maximum likelihood estimate

[0049]

[Equation 11]

And the variance σ ² is, for example, the maximum likelihood estimated value of the normal distribution.

[0051]

[Equation 12]

Is used.

In addition to the probability density function shown in the above equation 10,

[0054]

[Equation 13]

The mean value m and the variance σ in the equation may be
^{For 2} , each may use the maximum likelihood estimated value as defined by the above-mentioned mathematical expression 10.

Subsequently, in this selecting means, with respect to the output from the input physical model, a function of a previously defined probability density function f (x, m, σ ² ) or g (x, m, σ ² ) A value is calculated and this value is compared with a predetermined threshold value a (constant). At this time, if f (x, m, σ ² ) <a or g (x, m, σ ² ) <a as follows, the output data from the newly input physical model is optimal. Data that does not meet the above conditions is rejected, and it is rejected.

Next, in the second step, the degree of contribution to the optimization is determined for the data group determined by the selecting means as the data to be used for the optimization in the first step, and The parameter update amount is calculated for each parameter, and the parameter value before updating each parameter is updated by the update amount corrected according to the calculated contribution degree to obtain the parameter value of each parameter in the physical model.

This is because the error between the output obtained from the physical model and the output obtained from the above-mentioned processing process, or the evaluation function expressing the difference given by the absolute value of the error becomes the minimum value for each parameter. The update amount of the parameter value is used, and the new parameter value of each parameter is obtained by adding a value obtained by multiplying the parameter value before updating by the degree of contribution to optimization and the update amount.

Specifically, the above-mentioned second step is performed by the optimizing means in the signal processing apparatus according to the present invention. First, the function value f (x, m,
As a function of σ ² ) or g (x, m, σ ² ), a function L that determines contributions L _f and L _g to the optimization is defined as follows.

L _f = L (f (x, m, σ ² )) or L _g = L (g (x, m, σ ² )) Then, as shown below, the output obtained from the physical model and Evaluation function E representing an error from the output obtained from the above processing process or a difference given by the absolute value of the error
E _j = (X _j −T _j ) ² or

[0061]

[Equation 14]

It is defined by In the formula, X _j is the output from the physical model, and T _j is the output from the processing process.

Here, the above physical model is a function G, and the parameter value of each parameter to be optimized is P _i (i =
1,2, ..., m), it can be expressed by G≡G (P _i ).

Therefore, a new parameter value P _i (t + Δt) of each parameter is obtained from the contribution L _f or L _g to the optimization and the update amount of each parameter obtained using the generalized delta rule. As shown below, it is determined by updating the parameter value before the update by the update amount corrected according to the contribution degree.

P _i (t + Δt) = P _i (t) + L _* ∂
G (P _i ) / ∂P _{i where} L _* is the contribution L _f or L _g .

[0066]

In the signal processing method and the apparatus therefor according to the present invention, the selecting means for implementing the first step selects the data to be optimized prior to the optimization of each parameter in the physical model. ing.

That is, the data used for optimizing this data by discriminating and rejecting the data that is clearly deviated from the distribution state of the output data from the physical model which is the data to be optimized. It makes it possible to eliminate the influence on the optimization due to the presence in the group.

Specifically, for example, as shown in FIG.
By rejecting the data corresponding to the portion deviating from the data distribution that should originally exist (indicated by a in the figure) from the optimization target data, it is possible to perform optimization from only significant data.

Further, when focusing on the data group used for optimization in this figure, by considering the frequency with respect to each data value as the degree of contribution to optimization, the most distributed data is given the highest priority, The small distribution data can determine the update rate as having the degree of influence commensurate with the frequency, so that it is possible to obtain an efficient and optimum optimization result.

Actually, the contribution is not determined from the frequency, and the above description has been made to facilitate visual recognition, but the contribution calculated by the optimizing means is , Equivalently there is a relative agreement with frequency.

[0071]

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 is omitted.

FIG. 1 is a diagram showing the configuration of a signal processing apparatus B for implementing the signal processing method according to the present invention. Instead of the optimizing means 5 in the conventional signal processing apparatus shown in FIG. 9, the physical model 3 is used. It is characterized by optimizing each parameter in.

[0073] That is, in the signal processing device B, the relative output X _j from the physical model 3, the optimization of the physical model 3 performed for the output X _j is more approximate to the output T _j of processes 1 ( Selection means 6 for judging whether or not the data should be used for tuning each parameter in this physical model to an optimum value, and the degree of contribution to the optimization for the data group adopted by this selection means 6. And the update amount of each parameter is calculated, and the parameter value before updating each parameter is updated by the updated amount corrected in accordance with the calculated contribution degree.

In particular, the selecting means 6 judges whether or not the output X _j from the physical model 3 is data to be used for optimization, and whether or not this output X _j is data to be used for optimization. This is performed by calculating a function value of a probability density function defined in advance as an evaluation function for determining, and comparing this function value with a predetermined threshold value (constant).

The optimization means 7 evaluates the difference between the output X _j obtained from the physical model 3 and the output T _j obtained from the processing process 1 or the difference given by the absolute value of the error. The function E uses the minimum value of each parameter as the update amount of each parameter value, and the new parameter value of each parameter is obtained by multiplying the parameter value before update by the degree of contribution to optimization and the update amount. Each value is calculated by adding the values.

Next, the operation of the signal processing apparatus B will be described with reference to FIG.
3 and the flowchart of FIG.

First, as shown in FIG. 2, the selecting means 6 in the signal processing apparatus B inputs the output X _j obtained from the physical model 3 (step ST1), and the output X _j is as follows. , The data value input in the past is x
_i (i = 1,2, ..., N), and a probability density function indicating the distribution of data is defined in advance.

[0078]

[Equation 15]

At this time, X _j in the equation is the j-th output data from the physical model to be input in the future, m is the average value of the data values input in the past, σ ² is the variance thereof, and the average value m Is the maximum likelihood estimate of the normal distribution

[0080]

[Equation 16]

And the variance σ ² is, for example, the maximum likelihood estimated value of the normal distribution.

[0082]

[Equation 17]

Is used.

In addition to the probability density function shown in the above equation 15,

[0085]

[Equation 18]

The mean value m and the variance σ in the equation may be
² may use the maximum likelihood estimated value as defined by the above-mentioned mathematical expression 15.

Subsequently, in the selecting means 6, with respect to the output X _j from the input physical model, the probability density function f
A function value of (X _j , m, σ ² ) or g (X _j , m, σ ² ) is calculated (step ST2), and this value is compared with a predetermined threshold value a (constant) (step). ST3).

At this time, if the following conditions are satisfied, f (x, m, σ ² ) <a or g (x, m, σ ² ) <a The selecting means 6 selects the data to be used for optimization. However, the data that does not satisfy the above conditions is rejected (step ST5), and the data to be used for optimization is selected.

Then, as shown in FIG. 3, the optimizing means 7 in the signal processing apparatus B together with the data X _j adopted by the selecting means 6 together with the function values f (x, m, σ ² ),
Alternatively, input g (x, m, σ ² ) (step ST
6) As shown below, the function L that determines the contributions L _f and L _g to the optimization is defined, and the contributions L _f and L _g are calculated (step ST7).

L _f = L (f (x, m, σ ² )) or L _g = L (g (x, m, σ ² )) Then, the output obtained from the physical model 3 as shown below. And the error between the output obtained from the above process 1,
Alternatively, the evaluation function E expressing the difference given by the absolute value of the error is expressed as E _j = (X _j −T _j ) ² or

[0091]

[Formula 19]

By defining as described above, the update amount of each parameter value in the physical model 3 is calculated (step ST8).
In the equation, j indicates the jth data, and X
_j is an output from the physical model 3, and T _j is an output from the processing process 1.

Here, the above physical model is a function G, and the parameter value of each parameter to be optimized is P _i (i =
1,2, ..., m), it can be expressed by G≡G (P _i ).

Therefore, the new parameter value P _i (t + Δt) of each parameter is calculated from the contribution L _f or L _g to the optimization and the update amount of each parameter obtained using the generalized delta rule. , As shown below, it is determined by updating the parameter value before update by the update amount corrected according to the contribution degree (step ST
9).

P _i (t + Δt) = P _i (t) + L _* · ∂
G (P _i ) / ∂P _{i where} L _* is the contribution L _f or L _g .

Further, the evaluation function for obtaining the update amount of each parameter value and its update rule are, for example, Takahashi et al.
(IEICE Transactions A, Vol. J76-A, N
o. 3, pp. 297-302, March 1993), the following evaluation function e (t) is defined.

E (t) = r (t) -y (t) At this time, r (t) is a reference signal (corresponding to the output of the processing process 1) and y (t) is an adaptive filter (corresponding to the physical model 3). ) Output signal (corresponding to the output from the physical model 3)
And the output signal y (t) is expressed by the following equation.

Y (t) = W (t) ^T · X (t) where W (t) = {w ₁ (t), w ₂ (t), ...} ^T X (t) = {x ₁ (T), x ₂ (t), ...} In the ^T expression, W (t) is the coefficient w _i (t) of the adaptive filter (i = 1,
, ...) is a coefficient vector, X (t) is an input vector x _i (t) (i = 1,2, ...) Input to the adaptive filter, and the subscript T is a vector transpose. Is shown.

Each coefficient is updated as follows, for example.

W (t + 1) = W (t) +2 μ · e (t) · X (t) where μ is a constant called a step size. When the maximum eigenvalue of the correlation matrix of the input signal is λ _MAX , this step size μ must be 0 <μ <1 / 2λ _MAX .

Further, in this document, a method of using a step size which changes with time is proposed instead of the step size μ which is a fixed value. The coefficient update rule is shown below.

[0102]

[Equation 20]

Here, β is a step size that does not depend on the input signal, and its value is 0 <β <2.

As a method of reducing the amount of calculation for updating the coefficient, an algorithm for updating the coefficient using the sign of the input signal or the error signal is also proposed.

This is as a coefficient updating method: W (t + 1) = W (t) + μ.sgn [e (t)]. X
(T) W (t + 1) = W (t) + μ · e (t) · sgn [X
(T)] W (t + 1) = W (t) + μ · sgn [e (t)] · sgn
[X (t)] As a method of using the sign of the input signal,

[0106]

[Equation 21]

Has been proposed. Where sgn [X
(T)] is sgn [X (t)] = {sgn [x ₁ (t)], sgn [x ₂
(T)], ...} ^T L is the number of tabs.

Next, as an application example of the present invention, a case where the actual treatment process 1 is a rolling process in a steel plant will be described.

FIG. 4 is a diagram for explaining a rolling situation in a rolling process which is a simulation target by showing a cross section of an iron plate which is a material.

FIG. 11A shows rolling (referred to as etching rolling) from the left and right direction of the plate width WI (direction from the edge of the plate to the center), 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 and right directions, the edge portion is crushed so as to protrude in the thickness HI direction (the portion where the white background portion protrudes in the figure), and the closer to the center, the less the effect of etching rolling. .

Then, in the horizontal direction (direction from the center of the plate to the edge) with respect to the edging-rolled iron 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 horizontally rolled by the horizontal rolling (the process of FIG. 2B to FIG. 2C), the horizontal rolling causes the horizontal rolling as shown in FIG. The white background portion (referred to as a dog bone) in FIG. 4) contributes to 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 physical model 3 is shown below.

WO = WH + WD + WE where:

[0115]

[Equation 22]

[0116]

[Equation 23]

In the equation, each parameter is: WO: output of the physical model 3 WH: amount of width spread of horizontal rolling in the shaded part WD: amount of width spread of horizontal rolling in the white background part HI: entrance side plate thickness HO: exit side plate Thickness WE: plate width after edger rolling LD: projected contact arc length RR: horizontal roll radius RE: edger roll radius

That is, the width WO finally rolled.
The plate WE after edging rolling is represented by the sum of the contribution WD of the dog bone portion to horizontal rolling and the contribution WH of the rectangular cross-section portion to horizontal rolling.

The signal processing apparatus B for realizing the signal processing method according to the present invention uses the above rolling model as the physical model 3 and outputs the output of the physical model 3 with high precision in a strip width WO (processing process). Equivalent to the output obtained from 1)
It is characterized by performing automatic optimization to approximate to.

The physical model 3 has nine regression parameters. Specifically, 1.6
40, 0.376, 0.016, 0.015, 1.87
7, 0.063, 0.989, and 7.591. Let these parameters be P ₁ , ..., P ₉ from the beginning, and let the WH part and the WD part of the physical model 3 shown in Equation 22 be functions f and g, respectively.

As a result, the function f has the parameter P
_{As a} function having ₁ to P ₄ as an argument, and the function g is considered to be a function having parameters P ₅ to P ₉ as arguments, respectively. The operation of the optimizing means 7 will be described assuming that the selection has already been completed.

Assuming that the physical model 3 is composed of these two functions, the rolling result actually rolled with respect to the final strip width WO (output X _j of the physical model 3) obtained from the above equation. Is the value measured by a sensor, etc.
Letting R (output T _j of the processing process 1) be WO-WR as a prediction error, and the optimizing means 7 optimizes the parameter values of the respective parameters P ₁ , ..., P ₉ for minimizing this value. To convert.

Therefore, the evaluation function E is defined as follows for the above prediction error.

E _j = (WO _j -WR _j ) ² = (WO _j (P _ij ) -WR _j ) ² ≡E _j (P _ij ) In the formula, j represents the j-th input data. , I
Indicates the parameter number (i = 1, ..., 9).

Next, the update amount is calculated for each of the parameters dP _ij / dt∝dE (P _ij ) / dP _ij by the following generalized delta rule, and a new parameter value P _ij (t + Δt) is calculated.

DP _ij / dt = −η · dE (P _ij ) / dP _ij P _ij (t + Δt) = P _ij (t) + η · dP _ij / dt + ε
D ² P _ij / dt ^{2 In} the formula, η is a learning coefficient, ε is an inertia coefficient, and this learning coefficient η is updated with a value obtained from the evaluation function E.

Further, since each of the parameters P ₁ , ..., P ₉ in the physical model 3 can learn the optimum value for each of positive and negative, it is possible to optimize under the condition having the double degree of freedom. Becomes

Specifically, since the parameters x _i can take positive and negative values for the physical model (Y / X) ^Xi , the values of (Y / X) ^Xi and (Y / X) ^{| Xi |} It will be either.
However, if the relationship between the numerator and denominator of this model (Y / X) is fixed, further operation ((Y / X) ¹⁰ ) ^Xi should be performed to obtain a consistent optimal solution. Is possible.

The result of solving the differential equation obtained by the generalized delta rule as described above is shown below.

[0130]

[Equation 24]

[0131]

[Equation 25]

[0132]

[Equation 26]

[0133]

[Equation 27]

[0134]

[Equation 28]

[0135]

[Equation 29]

[0136]

[Equation 30]

[0137]

[Equation 31]

[0138]

[Equation 32]

In the equations, the functions f and g are functions obtained by replacing the parameters in the equations 22 and 23 with the parameters P ₁ , ..., P ₉ respectively as described above, and the bar P is the parameter P. It is a vector having _{1 to} P ₄ and P _{5 to} P ₉ as components, and especially initial values of these parameters are set as follows, respectively.

[0140] Note that FIG. 5 is a diagram showing the optimization process performed by the optimization means 7, and in FIG. 5 (a), the evaluation function E (= (WO-WR) ² is associated with the number of optimizations. (B) is a diagram showing how the error represented by () decreases, and FIG. 8B is a diagram showing a convergence process of the variance of the error with respect to the number of optimizations performed in the same manner.

Next, FIGS. 6 to 8 are diagrams and histograms for explaining the effect of the present invention in comparison with the optimization in the conventional signal processing apparatus A. Particularly, FIG. 6 is a physical diagram before optimization. FIG. 7 shows the error distribution of the prediction output obtained from the model 3, and FIG. 7 shows the physical model 3 when optimized by the optimizing means 5 which optimizes by the conventional regression method shown in FIG.
The error distribution of the prediction output of is shown. Further, FIG. 8 shows the error distribution of the predicted output of the physical model 3 when optimized by the signal processing apparatus B for realizing the signal processing method according to the present invention.

Here, in FIG. 6A in which the error distribution of the prediction output obtained from the physical model 3 before optimization is plotted, the data 8a and the prediction error which are extremely distant from the data in the vicinity of the plate width 1600 mm are predicted. The effect of the present invention will be described below, focusing on the data 8b having a small number.

First, as shown in FIG. 7A, in the optimization performed by the optimizing means 5 in the conventional signal processing apparatus A,
Due to the influence of the group 8a whose prediction errors are far apart, the error of the data 8b having a small prediction error is large (FIG. 6).
(The part 8b in (a) moves to 8c).

On the other hand, according to the present invention, as shown in FIG. 8 (a), the selecting means 6 rejects the data 8a having an extremely large error in advance before the optimization and selects the data to be used for the optimization. Therefore, the data group having a small error by the optimization means 7 (portion 8b in FIG. 6A)
It can be seen that an optimization result of further compressing the prediction error (the portion 8b in FIG. 6A moves to 8d) is obtained. That is, in the present invention, the data far away from the population (portion 8a in FIG. 6A) is considered to be a prediction output based on erroneous information from some measurement system, and these are output in advance by the selection means 6. An optimum optimum result can be obtained by using only the excluded data group for the optimization of the physical model 3 and determining how important the individual data used for this optimization is the data. It is shown that.

Note that each of FIGS. 6 to 8 (a).
Shows the plate width on the horizontal axis, and the error from the actual value for each plate width is taken on the vertical axis. Also, in the histograms shown in each of the diagrams (b), the horizontal axis indicates the previous prediction error, The vertical axis represents the frequency of how many data have respective prediction errors (each figure (b) is a projection of each figure (a) in the vertical axis direction).

[0146]

As described above, according to the present invention, prior to the optimization of the physical model that expresses the actual processing process by the mathematical expression (the optimum value of each parameter is determined), the optimization is performed in advance. The physical model is optimized by determining whether or not it is the data to be used and using only the data to be used for this optimization. Further, there is an effect that the output of the physical model that is similar to the output of the processing process is obtained.

[Brief description of drawings]

FIG. 1 is a diagram showing a configuration of an embodiment of a signal processing device for realizing a signal processing method according to the present invention.

FIG. 2 is a flow chart for explaining the operation of the selecting means in the signal processing device for realizing the signal processing method according to the present invention.

FIG. 3 is a flowchart for explaining the operation of the optimizing means in the signal processing device for realizing the signal processing method according to the present invention.

FIG. 4 is a diagram for explaining the operation when the signal processing method and apparatus according to the present invention are applied to a steel rolling process.

FIG. 5 is a diagram showing a convergence process of an error and an error variance with respect to the number of times optimization is performed by the signal processing method and the apparatus according to the present invention.

FIG. 6 is a diagram and a histogram in which data used for optimization by a signal processing device that realizes the signal processing method according to the present invention and a conventional signal processing device are plotted.

FIG. 7 is a diagram and a histogram for explaining an effect of optimization by a conventional signal processing device.

8A and 8B are a diagram and a histogram for explaining the effect of optimization by the signal processing method and apparatus according to the present invention.

FIG. 9 is a diagram showing a structure of a conventional signal processing device.

FIG. 10 is a diagram showing a probability distribution of data to be optimized.

[Explanation of symbols]

1 ... Processing process, 2 ... Error evaluation means, 3 ... Physical model, 4 ... Desired characteristic, 6 ... Selection means, 7 ... Optimization means, B
... Signal processing device.

Claims (7)

[Claims] 1. In the optimization of each parameter in a calculation formula, a first step of judging whether or not the output from the calculation formula is data to be used for optimization, and the first step. By evaluating the error between the output of the calculation formula in which the data determined to be the data to be used for optimization in the process is input and the output for constructing a function in the calculation formula, the contribution to the optimization of the data is calculated. A signal processing method comprising a second step of calculating a new parameter value of each parameter in consideration. 2. The determination performed in the first step is a probability density defined in advance as an evaluation function for determining whether or not the output from the calculation formula is data to be used for optimization. 2. The signal processing method according to claim 1, wherein the function value of the function is calculated and the function value is compared with a predetermined threshold value. 3. The new parameter value of each parameter determined in the second step is added with a value obtained by multiplying the parameter value before update by the update amount obtained by evaluating the contribution and the error. The signal processing method according to claim 1 or 2, wherein 4. The optimization of each parameter in the physical model, which is performed so as to further approximate the output of the physical model obtained by approximating the actual processing process to be simulated by an equation to the output of the processing process, Calculate a function value of a probability density function defined in advance as an evaluation function for determining whether the output is data to be used for optimization with respect to the output, and compare the function value with a predetermined threshold value. The first step of determining whether or not the output is data to be used for optimization, and the optimization of the data group determined to be data to be used for optimization in the first step A second process of determining the contribution degree, calculating the update amount of each parameter, and updating the parameter value of each parameter before update by the update amount corrected in accordance with the calculated contribution degree. Signal processing method comprising and. 5. The new parameter value of each parameter determined in the second step is obtained by adding a value obtained by multiplying the parameter value before update by the contribution degree and the update amount. Item 4. The signal processing method according to item 4. 6. A signal processing apparatus for optimizing each parameter of a physical model, which is adapted to further approximate an output of a physical model obtained by approximating an actual processing process to be simulated by a mathematical expression, to the output of the processing process. A function value of a probability density function defined in advance as an evaluation function for determining whether or not the output from the physical model should be used for optimization is calculated, and the function value and a predetermined threshold value are calculated. Selecting means for determining whether or not the output is data to be used for optimization by comparing with, and determining the degree of contribution to optimization for the data group adopted by the selecting means, and A signal processing device provided with an optimization means for calculating the update amount of each parameter and updating the parameter value of each parameter before update by the update amount corrected according to the calculated contribution degree. . 7. The optimization means obtains a new parameter value of each of the parameters by adding a value obtained by multiplying the parameter value before update by the contribution degree and the update amount. The signal processing device described.