Data processing: generic control systems or specific application – Generic control system – apparatus or process – Optimization or adaptive control
Reexamination Certificate
2000-04-19
2004-10-19
Picard, Leo (Department: 2125)
Data processing: generic control systems or specific application
Generic control system, apparatus or process
Optimization or adaptive control
C700S173000, C706S023000, C706S052000
Reexamination Certificate
active
06807449
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to a method for controlling and preconfiguring a steelworks or parts of a steelworks. In this context, the term parts of a steelworks is intended to mean rolling mill trains, rolling stands, continuous or strip casting systems and units for heat treatment or cooling.
The present invention also relates to a method for controlling and/or preconfiguring a rolling stand or a rolling mill train for rolling a strip, the rolling stand or the rolling mill train being controlled and/or preconfigured by means of a model of the rolling stand or the rolling mill train, the model having at least one neural network whose parameters are matched or adapted to the actual conditions in the rolling stand or in the rolling mill train, in particular to the properties of the strip.
BACKGROUND INFORMATION
In order to control and preconfigure rolling stands or a rolling mill train for rolling a strip, models may be used which have at least one neural network whose parameters are matched or adapted to the actual conditions in the rolling stand or in the rolling mill train, in particular to the properties of the strip. Model-assisted control or preconfiguration of this type is in particular possible for applications as described in DE 41 31 765, EP 0 534 221, U.S. Pat. No. 5,513,097, DE 44 16 317, U.S. Pat. No. 5,600,758, DE 43 38 608, DE 43 38 615, DE 195 22 494, DE 196 25 442, DE 196 41 432, DE 196 41 431, DE 196 42 918, DE 196 42 919, DE 196 42 921. If they are adapted on-line, neural networks for these applications are adapted at constant adaptation rates. This means that, on the basis of each strip which is rolled, the error function for this strip is calculated. The leave of this error function is then determined and, with a view to a gradient optimization, a procedure is adopted whereby the error function is reduced by the chosen adaptation rate. It has been shown that, using on-line adaptation, the term on-line adaptation being intended to mean the adaptation of a neural network on the basis of a strip which is rolled, the quality of rolled steel is significantly improved. Difficulties are, however, found in terms of reliability problems pertaining to the convergence during the adaptation. If, because of deficient adaptation to malfunctioning, incorrect control or deficient preconditioning arise, this may lead to large losses for the application on account of inferior rolled steel or damage to the rolling mill train. Furthermore, because of the high investment costs for a rolling mill train, downtimes are very expensive. This being the case, the adaptation of neural networks for the control or preconfiguration of rolling stands or rolling mill trains is problematic.
SUMMARY
An object of the present invention is to provide a method for making the control or preconfiguration of a steelworks or parts of a steelworks more reliable. It is furthermore desirable to improve the accuracy of the model values determined by means of a neural network.
The object is achieved according to the invention by providing a method in which the rate at which the parameters are matched or adapted to the actual conditions in the rolling stand or in the rolling mill train, in particular to the properties of the strip, is varied. It is in this way possible, for example, to distinguish whether the neural network has already properly mastered the function to be approximated at the corresponding point, whether the data point belongs to an infrequent event, that is to say to steel which is rarely rolled, or whether, because of a measuring error or an error in the subsequent calculation, the data point to be trained is in fact completely unusable. This leads to much more robust adaptation. In an advantageous embodiment of the present invention, the rate at which the parameters are matched or adapted to the actual conditions in the rolling stand or in the rolling mill train, in particular to the properties of the strip, is varied as a function of the information density, in particular the training data pertaining to strips of the same or a similar type.
The information density D is in this case an (abstract) measure of how much information is present at a given point in the input space (typically, how many strips of the same or a similar quality have already been rolled). An illustrative embodiment for a definition of the information density is
D
(
x
n
)
=
∑
k
=
1
sizenet
b
k
(
x
n
)
D
k
(
x
n
)
D(X
n
) is the estimate of the information density for point xn, after treating all the patterns x
1
to x
n−1
. b
k
(x
n
) is the activity of the k-th neuron in the hidden plane or the hidden planes of the neural network on application of the pattern x
n
. D
k
(x
n
) is the estimate of the local information density at the site of the k-th neuron, after processing all patterns x
1
to x
n−1
. sizenet corresponds to the number of neurons in the hidden plane or the hidden planes of the neural network. b
k
is calculated from
b
k
(
x
n
)
=
exp
(
-
1
2
(
x
-
μ
)
T
∑
-
1
(
x
-
μ
)
)
with
x
=
[
x
1
x
2
⋮
x
n
]
μ
=
[
μ
1
μ
2
⋮
μ
n
]
and
∑
-
1
=
[
1
2
0
…
0
σ
1
0
1
2
⋮
σ
2
⋮
⋰
0
…
1
2
σ
n
]
&mgr;i being the expected value and &sgr;
2
i
the variance of x
i
.
D
k
(x
n
) is calculated as:
D
k
(
x
n
)
=
I
k
(
x
n
)
I
(
x
n
)
I
k(x
n
) is the information accumulated locally over the entire history of all patterns x
n
to x
n−1
at the k-th neuron of the hidden plane or of the hidden planes of the neural network, I(x
n
) is the information similarly acquired overall in the network. I
k
(x
n
) is calculated as
I
k
(
x
n
)
=
∑
x
′
=
{
x
1
…
x
n
-
1
}
b
k
(
x
′
)
f
(
E
(
x
′
)
,
η
(
x
′
)
)
f is a function of the prognosis error E(x′) (see below) and the learning rate &eegr;(x′). It takes into account that, for the patterns learned in the past only with a low learning rate, there is only a small amount of information. In the simplest case, it would be possible to set
f
=1∀(
x′∈x
1
. . . x
n−1
)
For I(x
n
):
I
(
x
n
)
=
∑
k
=
1
sizenet
I
k
(
x
n
)
=
∑
x
′
=
{
x
1
…
x
n
-
1
}
f
(
E
(
x
′
)
,
η
(
x
′
)
)
Since, for all x′&egr;{x
1
. . . x
n−1
], then
∑
k
=
1
sizenet
b
k
(
x
′
)
=
1
In a further particularly advantageous embodiment of the present invention, the rate at which the parameters are matched or adapted to the actual conditions in the rolling stand or in the rolling mill train, in particular to the properties of the strip, is varied as a function of the expected error, in particular the average error over the entire adaptation phase or the average error over a long time interval during the adaptation.
The expected error F is, for example, the average error over the entire history at the point x
n
in space. It may, for example, be of the following form:
F
(
x
n
)
=
∑
k
=
1
sizenet
b
k
(
x
n
)
F
k
(
x
n
)
F
k
(x
n
) being the local expected error for the n-th pattern at the k-th neuron of the hidden plane of a neural network. If F
k
(x
n
) is given as
F
k
(
x
n
)
=
∑
x
′
=
{
x
1
…
x
n
-
1
}
b
k
(
x
′
)
E
(
x
′
)
f
(
E
(
x
′
)
I
k
(
x
n
)
Through multiplication of the error E(x′) with b
k
(x′), the numerator contains a measure of the local error. This error is divided by the local information density.
A further approach for calculating the expected error is for
Gramckow Otto
Malisch Frank-Oliver
Schlang Martin
Baker & Botts LLP
Picard Leo
Rao Sheela S.
Siemens Aktiengessellscaft
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