CN112099353B - Divergence constraint kernel discriminant analysis-based continuous casting billet subsurface slag inclusion defect prediction method - Google Patents

Divergence constraint kernel discriminant analysis-based continuous casting billet subsurface slag inclusion defect prediction method Download PDF

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CN112099353B
CN112099353B CN202010939878.7A CN202010939878A CN112099353B CN 112099353 B CN112099353 B CN 112099353B CN 202010939878 A CN202010939878 A CN 202010939878A CN 112099353 B CN112099353 B CN 112099353B
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宋执环
魏驰航
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Zhejiang University ZJU
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Abstract

The invention discloses a continuous casting billet subcutaneous slag inclusion defect forecasting method based on divergence constraint kernel discriminant analysis. Compared with the traditional algorithm, the method can greatly improve the accuracy of real-time prediction of the subsurface slag inclusion defect of the continuous casting billet.

Description

Divergence constraint kernel discriminant analysis-based continuous casting billet subsurface slag inclusion defect prediction method
Technical Field
The invention belongs to the field of industrial process control, and particularly relates to a continuous casting billet subsurface slag inclusion defect forecasting method based on divergence constraint kernel discriminant analysis.
Background
Continuous casting is an important process in the steel industry, in the continuous casting process, molten steel in a converter enters a crystallizer through a ladle and a tundish, and casting powder is added (the casting powder on the top of a molten steel page has the functions of heat preservation, secondary oxidation prevention of the molten steel, impurity absorption and the like). In the crystallizer, the molten steel is cooled and solidified into a soft steel blank with a certain blank shell thickness, then the soft steel blank is pulled and straightened by a straightener and a dummy bar device, and finally the soft steel blank is cut into a steel blank by a flame cutting machine; FIG. 1 is a schematic drawing of a continuous casting process. Subcutaneous slag inclusion is one of the most frequently occurring defects in the quality of a plurality of steel billets. The subsurface slag inclusion defect refers to that large, irregular and discontinuous slag is embedded on the surface of a casting blank or 2mm-10mm below the surface of the casting blank. In the continuous casting process, slag inclusion can influence the heat-conducting property of a primary blank shell, the thickness of a solidified shell is reduced, and the occurrence of steel leakage outside a crystallizer is easy to cause serious production accidents; in the subsequent process, the billet with slag in the skin can cause serious surface defects of hot rolled and cold rolled products, such as black lines, peeling, bulges and the like, which are the most main surface defects of high-quality cold rolled sheets. Therefore, the problem related to the subcutaneous slag inclusion defect is an important problem which needs to be solved urgently by steel companies, and deep research on the subcutaneous slag inclusion defect is carried out in academic circles and industrial circles all over the world.
The research on the defect of subcutaneous slag inclusion can be summarized into two types. The first type of research mainly analyzes and searches for the cause of the subcutaneous slag inclusion and attempts to reduce the incidence of the subcutaneous slag inclusion defect by controlling the factors, but because the continuous casting process has complex mechanism and difficult control, the current continuous casting process control system cannot completely eliminate the subcutaneous slag inclusion defect as described above. The second type of research aims to establish a quantitative relation (namely a model) between the continuous casting process operation variables and the slag inclusion defects by using process data, predict whether the slag inclusion defects occur on line, classify and process the casting blanks predicted to have the slag inclusion defects, and avoid the casting blanks from entering a subsequent rolling process, so that the aims of reducing the rejection rate and improving the production efficiency in the rolling process are fulfilled. The data-driven method does not need very deep process mechanism knowledge, has rich functions, high flexibility, strong adaptability and low investment and maintenance cost, has great advantages compared with other methods, and is a research hotspot in academia and industry. However, because the continuous casting process and the production data characteristics are very complex, the existing data-driven continuous casting billet subsurface slag inclusion detection method has the problems of low precision, high missing report rate and false report rate and the like, and the application effect of the method still cannot meet the requirements of actual production.
Disclosure of Invention
Aiming at the problem of the existing data-driven continuous casting billet subsurface slag inclusion defect prediction, the invention provides a continuous casting billet subsurface slag inclusion defect prediction method based on divergence constraint kernel discriminant analysis, which comprises the following steps:
a continuous casting billet subcutaneous slag inclusion defect forecasting method based on divergence constraint kernel discriminant analysis comprises the following steps:
the method comprises the following steps: collecting data under normal working conditions of the continuous casting production process and data when slag inclusion faults occur to obtain a training sample set for modeling
Figure BDA0002673255000000021
Wherein xi∈RPN is the total number of training samples, P is the number of process variables, R is the set of real numbers, yiRepresents xiCategory information of (1);
step two: preprocessing and normalizing the training sample set;
step three: in a reconstructed kernel Hilbert space, a divergence constraint kernel discriminant analysis model is established, and the specific algorithm is as follows:
(1) for each category t, a representative point is selected
Figure BDA0002673255000000022
(2) Suppose sample point xiThe defect prediction result is f (x)i) For each category t, calculating the intra-class divergence
Figure BDA0002673255000000023
Figure BDA0002673255000000024
(3) The total intra-class divergence σ is calculated according to the following equationW
Figure BDA0002673255000000025
Wherein T is the number of categories;
(4) the total between-class divergence σ is calculated according to the following equationB
Figure BDA0002673255000000026
(5) Based on sigmaWAnd σBCalculating the divergence constraint Re according to the following formulaScatter
Figure BDA0002673255000000027
(6) Construction of the loss function V (y)i,f(xi))；
(7) Establishing divergence constraint kernel discriminant analysis model
Figure BDA0002673255000000028
Wherein HκReconstructing a nuclear hilbert space, wherein gamma is a weight coefficient;
step four: calculating a solution of a divergence constraint kernel discriminant analysis model;
step five: establishing a slag inclusion defect real-time forecasting system;
step six: collecting new process data
Figure BDA0002673255000000029
And carrying out the same pretreatment and normalization with the modeling data to obtain xnew；
Step seven: x is to benewSubstituting the slag inclusion defect into a real-time forecasting system to calculate and obtain a slag inclusion defect forecasting result f (x)new)。
Further, the representative points in the third step
Figure BDA0002673255000000031
The selection is carried out according to the following steps:
(1) for each category t, calculate its mean point
Figure BDA0002673255000000032
GtSet of all samples of the class t, NtIs GtThe number of sampling points contained;
(2) at GtTo select and
Figure BDA0002673255000000033
the nearest modeling point as a class representative point of the class t
Figure BDA0002673255000000034
Further, the fourth step is specifically realized by the following sub-steps:
(1) using the representation theorem of the reconstructed nuclear Hilbert space, i.e.
Figure BDA0002673255000000035
Will sigmaW、σB、ReScatterThe transformation is as follows
Figure BDA0002673255000000036
Wherein α ═ α1LαN]TK is a kernel matrix;
(2) constructing the loss function by selecting a least squares method, i.e.
Figure BDA0002673255000000037
And converts it into
V(yi,f(xi))＝(y-Kα)T(y-Kα) (8)
Where K is the kernel matrix and y ═ y1L yN]T；
(3) Converting the optimization f problem into an optimization alpha value to obtain an optimization problem:
J＝(y-Kα)T(y-Kα)+γαTVα (9)
(4) and solving the optimization problem.
Further, the analytical solution α for solving the optimization problem*The method comprises the following specific steps:
(1) using the representation theorem of the reconstructed nuclear Hilbert space, the original optimization problem is transformed into the following optimization problem
J＝(y-Kα)T(y-Kα)+γαTVα (10)
(2) Is obtained according to the following formula
Figure BDA0002673255000000041
Figure BDA0002673255000000042
(3) Order to
Figure BDA0002673255000000043
Working up to obtain an analytic solution of alpha
α*＝[KK+γV]-1Ky (12)
Further, the step five is specifically realized by the following sub-steps:
(1) according to the representation theorem of the reconstructed nuclear Hilbert space, if the sample point to be detected is xnewThe prediction result of slag inclusion defect is f (x)new) Then a real-time slag inclusion defect forecasting system is established as
Figure BDA0002673255000000044
Further, the loss function constructed in step three may be implemented in any one of the following four ways:
(1) least square method
Figure BDA0002673255000000045
(2) Hinge loss method
Figure BDA0002673255000000046
(3) Cross entry loss method
Figure BDA0002673255000000047
(4) Exponental loss method
Figure BDA0002673255000000048
The invention has the following beneficial effects:
(1) the prediction of the subsurface slag inclusion defect of the continuous casting slab based on the traditional discriminant analysis or classification method usually only focuses on inter-class divergence and ignores intra-class divergence containing important data characteristics. Different from the traditional method, the continuous casting billet subsurface slag inclusion defect forecasting method based on divergence constraint kernel discriminant analysis simultaneously considers the intra-class divergence and the inter-class divergence: on the one hand, the intra-class divergence is minimized in the reconstructed nuclear hilbert space, so that data points of the same class are as close as possible in the reconstructed nuclear hilbert space; on the other hand, the inter-class divergence is maximized in the reconstructed nuclear hilbert space, so that the data points of the different classes are separated in the reconstructed nuclear hilbert space as much as possible. Based on the method, divergence constraint kernel discriminant analysis can excellently complete classification and continuous casting billet subsurface slag inclusion defect prediction tasks.
(2) In the continuous casting billet subcutaneous slag inclusion defect forecasting method based on divergence constraint kernel discriminant analysis, the discriminant information in the modeling data is innovatively used for calculating the intra-class divergence and the inter-class divergence in the reconstructed kernel Hilbert space, and the two divergences are weighted and fused to be used as regular terms of an optimization problem.
(3) The continuous casting billet subsurface slag inclusion defect forecasting method based on divergence constraint kernel discriminant analysis greatly simplifies model optimization solving difficulty by using the representation theorem of a reconstructed kernel Hilbert space, can directly calculate to obtain a unique analytic solution, is not disturbed by local extreme values, and does not need complex iterative solving steps.
(4) Some traditional discriminant analysis or classification methods assume that process variables are in linear relation, such as linear discriminant analysis, secondary discriminant analysis, logistic regression and the like, and variable relations in the actual process are often nonlinear, so that continuous casting billet subsurface slag inclusion defect prediction based on the methods cannot achieve good effects in actual application. Different from the traditional methods, the divergence constraint kernel discriminant analysis method solves the nonlinear variable relation of process data by using a kernel projection mode, so that the result obtained by the continuous casting billet subcutaneous slag inclusion defect forecasting method based on divergence constraint kernel discriminant analysis is closer to reality.
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Fig. 1 is a schematic view of a continuous casting process in the background art.
FIG. 2 is a flow chart of a method of an embodiment of the present invention.
In the figure, A is molten iron, B: solidified iron, C: mold flux, D: water-cooled copper plate, E: refractory material, 1: ladle, 2: plug, 3: tundish, 4: ladle shroud, 5: casting mold, 6: rolling mill, 7: turning area, 8: ladle shroud, 9: mold water level, 10: meniscus, 11: cold rolling unit, 12: slab, 13: a flame cutting machine.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments, and the objects and effects of the present invention will become more apparent, it being understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
As shown in figure 2, the continuous casting billet subcutaneous slag inclusion defect forecasting method based on divergence constraint kernel discriminant analysis firstly collects normal working condition data and slag inclusion fault data in the continuous casting production process, establishes inter-class divergence and intra-class divergence, establishes a divergence constraint kernel discriminant analysis model by combining a loss function, then obtains a model analysis solution by utilizing the Reresenter Theorem calculation, and establishes a slag inclusion defect real-time forecasting model. The method comprises the following specific steps:
the method comprises the following steps: collecting data under normal working conditions of the continuous casting production process and data when slag inclusion faults occur to obtain a training sample set for modeling
Figure BDA0002673255000000051
Wherein xi∈RPN is the total number of training samples, P is the number of process variables, R is the set of real numbers, yiRepresents xiCategory information of (1);
step two: preprocessing and normalizing the training sample set;
step three: in a reconstructed kernel Hilbert space, a divergence constraint kernel discriminant analysis model is established, and the specific algorithm is as follows:
(1) for each category t, a representative point is selected
Figure BDA0002673255000000061
As one of the embodiments, the point is represented
Figure BDA0002673255000000062
The selection is carried out according to the following steps:
calculating the mean value point of each category t
Figure BDA0002673255000000063
GtSet of all samples of the class t, NtIs GtThe number of sampling points contained;
② in GtTo select and
Figure BDA0002673255000000064
the closest modeling point is used as a category representative point of the category t.
Figure BDA0002673255000000065
(2) Suppose sample point xiThe defect prediction result is f (x)i) For each category t, calculating the intra-class divergence
Figure BDA0002673255000000066
Figure BDA0002673255000000067
(3) The total intra-class divergence σ is calculated according to the following equationW
Figure BDA0002673255000000068
Wherein T is the number of categories;
(4) the total between-class divergence σ is calculated according to the following equationB
Figure BDA0002673255000000069
(5) Based on sigmaWAnd σBCalculating the divergence constraint Re according to the following formulaScatter
Figure BDA00026732550000000610
(6) Construction of the loss function V (y)i,f(xi) ); the loss function takes any one of four ways:
(1) least square method
Figure BDA00026732550000000611
(2) Hinge loss method
Figure BDA00026732550000000612
(3) Cross entry loss method
Figure BDA0002673255000000071
(4) Exponental loss method
Figure BDA0002673255000000072
(7) Establishing divergence constraint kernel discriminant analysis model
Figure BDA0002673255000000073
Wherein HκReconstructing a nuclear hilbert space, wherein gamma is a weight coefficient;
step four: calculating a solution of a divergence constraint kernel discriminant analysis model;
as one embodiment, step four may be implemented by the following sub-steps:
(1) using the representation theorem of the reconstructed nuclear Hilbert space, i.e.
Figure BDA0002673255000000074
Will sigmaW、σB、ReScatterThe transformation is as follows
Figure BDA0002673255000000075
Wherein α ═ α1 L αN]TK is a kernel matrix;
(2) constructing the loss function by selecting a least squares method, i.e.
Figure BDA0002673255000000076
And converts it into
V(yi,f(xi))＝(y-Kα)T(y-Kα) (12)
Where K is the kernel matrix and y ═ y1 L yN]T；
(3) Converting the optimization f problem into an optimization alpha value to obtain an optimization problem:
J＝(y-Kα)T(y-Kα)+γαTVα (13)
(4) and solving the optimization problem.
As one of the embodiments, the analytical solution α for solving the optimization problem*The method comprises the following specific steps:
(1) using the representation theorem of the reconstructed nuclear Hilbert space, the original optimization problem is transformed into the following optimization problem
J＝(y-Kα)T(y-Kα)+γαTVα (14)
(2) Is obtained according to the following formula
Figure BDA0002673255000000081
Figure BDA0002673255000000082
(3) Order to
Figure BDA0002673255000000083
Working up to obtain an analytic solution of alpha
α*＝[KK+γV]-1Ky (16)
Step five: establishing a slag inclusion defect real-time forecasting system;
as one embodiment, step five is implemented by the following sub-steps:
(1) according to the representation theorem of the reconstructed nuclear Hilbert space, if the sample point to be detected is xnewThe prediction result of slag inclusion defect is f (x)new) Then a real-time slag inclusion defect forecasting system is established as
Figure BDA0002673255000000084
Step six: collecting new process data
Figure BDA0002673255000000085
And carrying out the same pretreatment and normalization with the modeling data to obtain xnew；
Step seven: x is to benewSubstituting the slag inclusion defect into a real-time forecasting system to calculate and obtain a slag inclusion defect forecasting result f (x)new)。
The validity of the proposed algorithm is verified in the following with an actual continuous casting process.
The actual continuous casting process contains 33 variables. In this embodiment, 6 representative plates are selected, and normal condition data and slag inclusion fault data are collected respectively to form 6 data sets, as shown in table 1. Table 1 also shows the degree of unbalance, i.e., the ratio of the positive sample ratio to the negative sample ratio, because the number of sampling points in the data set corresponding to different plates is greatly different from the ratio of the positive sample to the negative sample. All data points were collected at the industrial site and subsequently analyzed in the laboratory.
Table 16 representative panel-corresponding 6 datasets
Figure BDA0002673255000000086
Figure BDA0002673255000000091
For experimental verification, the data set in table 1 was partitioned according to 7:3, where the former was used to train the model and the latter was used to test the slag inclusion fault prediction effect. In order to verify the effect of the method, the embodiment selects the traditional data-driven classification model linear discriminant analysis, secondary discriminant analysis, logistic regression, support vector machine, limit lifting tree and the divergence constraint kernel discriminant analysis algorithm provided by the invention to distribute and establish the slag inclusion fault prediction model, and evaluates the prediction effect through the precision rate, the recall rate and F1 commonly used by the two classification problems. The prediction results of the above model are shown in table 2.
TABLE 2 slag inclusion fault prediction results of different methods
Figure BDA0002673255000000092
As is apparent from table 2, compared with the conventional prediction method, the continuous casting billet subsurface slag inclusion defect prediction method based on divergence constraint kernel discriminant analysis provided by the present invention obtains the optimal prediction results on data sets of different unbalances.
The simulation result verifies the effectiveness of the continuous casting billet subsurface slag inclusion defect prediction method based on divergence constraint kernel discriminant analysis, and compared with the traditional algorithm, the method can greatly improve the accuracy of the continuous casting billet subsurface slag inclusion defect real-time prediction and greatly improve the prediction performance.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and although the invention has been described in detail with reference to the foregoing examples, it will be apparent to those skilled in the art that various changes in the form and details of the embodiments may be made and equivalents may be substituted for elements thereof. All modifications, equivalents and the like which come within the spirit and principle of the invention are intended to be included within the scope of the invention.

Claims (5)

1. A continuous casting billet subcutaneous slag inclusion defect forecasting method based on divergence constraint kernel discriminant analysis is characterized by comprising the following steps:
the method comprises the following steps: collecting data under normal working conditions of the continuous casting production process and data when slag inclusion faults occur to obtain a training sample set for modeling
Figure FDA0003269863930000011
Wherein xi∈RPN is the total number of training samples, P is the number of process variables, R is the set of real numbers, yiRepresents xiCategory information of (1);
step two: preprocessing and normalizing the training sample set;
step three: in a reconstructed kernel Hilbert space, a divergence constraint kernel discriminant analysis model is established, and the method is specifically realized by the following substeps:
(1) for each category t, a representative point is selected
Figure FDA0003269863930000012
(2) Suppose sample point xiThe defect prediction result is f (x)i) For each category t, calculating the intra-class divergence
Figure FDA0003269863930000013
Figure FDA0003269863930000014
(3) The total intra-class divergence σ is calculated according to the following equationW
Figure FDA0003269863930000015
Wherein T is the number of categories;
(4) the total between-class divergence σ is calculated according to the following equationB
Figure FDA0003269863930000016
(5) Based on sigmaWAnd σBCalculating the divergence constraint Re according to the following formulaScatter
Figure FDA0003269863930000017
(6) Construction of the loss function V (y)i,f(xi))；
(7) Establishing divergence constraint kernel discriminant analysis model
Figure FDA0003269863930000018
Wherein HκReconstructing a nuclear hilbert space, wherein gamma is a weight coefficient;
step four: calculating a solution of a divergence constraint kernel discriminant analysis model;
the fourth step is specifically realized by the following substeps:
(1) using the representation theorem of the reconstructed nuclear Hilbert space, i.e.
Figure FDA0003269863930000021
Will sigmaW、σB、ReScatterThe transformation is as follows
Figure FDA0003269863930000022
Wherein α ═ α1…αN]TK is a kernel matrix;
(2) constructing the loss function by selecting a least squares method, i.e.
Figure FDA0003269863930000023
And converts it into
V(yi,f(xi))＝(y-Kα)T(y-Kα) (8)
Where K is the kernel matrix and y ═ y1…yN]T；
(3) Converting the optimization f problem into an optimization alpha value to obtain an optimization problem:
J＝(y-Kα)T(y-Kα)+γαTVα (9)
(4) solving the optimization problem;
step five: establishing a slag inclusion defect real-time forecasting system;
step six: collecting new process data
Figure FDA0003269863930000024
And carrying out the same pretreatment and normalization with the modeling data to obtain xnew；
Step seven: x is to benewSubstituting the slag inclusion defect into a real-time forecasting system to calculate and obtain a slag inclusion defect forecasting result f (x)new)。
2. The method for forecasting the subcutaneous slag inclusion defect of the continuous casting billet based on divergence constraint kernel discriminant analysis according to claim 1, wherein the representative points in the third step
Figure FDA0003269863930000025
The selection is carried out according to the following steps:
(1) for each category t, calculate its mean point
Figure FDA0003269863930000026
GtSet of all samples of the class t, NtIs GtThe number of sampling points contained;
(2) at GtTo select and
Figure FDA0003269863930000027
the nearest modeling point as a class representative point of the class t
Figure FDA0003269863930000031
3. The continuous casting billet subsurface slag inclusion defect prediction method based on divergence constraint kernel discriminant analysis according to claim 1, characterized in that an analytical solution alpha of an optimization problem is solved*The method comprises the following specific steps:
(1) using the representation theorem of the reconstructed nuclear Hilbert space, the original optimization problem is transformed into the following optimization problem
J＝(y-Kα)T(y-Kα)+γαTVα (10)
(2) Is obtained according to the following formula
Figure FDA0003269863930000032
Figure FDA0003269863930000033
(3) Order to
Figure FDA0003269863930000034
Working up to obtain an analytic solution of alpha
α*＝[KK+γV]-1Ky (12)。
4. The continuous casting billet subsurface slag inclusion defect forecasting method based on divergence constraint kernel discriminant analysis as claimed in claim 3, wherein the fifth step is specifically realized by the following sub-steps:
(1) according to the representation theorem of the reconstructed nuclear Hilbert space, if the sample point to be detected is xnewThe prediction result of slag inclusion defect is f (x)new) Then a real-time slag inclusion defect forecasting system is established as
Figure FDA0003269863930000035
5. The method for forecasting the subcutaneous slag inclusion defect of the continuous casting billet based on divergence constraint kernel discriminant analysis according to claim 1, wherein the loss function constructed in the third step is any one of the following four ways:
(1) least square method
Figure FDA0003269863930000036
(2) Hinge loss method
Figure FDA0003269863930000037
(3) Cross entry loss method
Figure FDA0003269863930000038
(4) Exponental loss method
Figure FDA0003269863930000041
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