WIDTH PREDICTION METHOD OF FINISHED ROLLED MATERIAL, WIDTH CONTROL METHOD OF FINISHED ROLLED MATERIAL, MANUFACTURING METHOD OF HOT-ROLLED STEEL SHEET, AND GENERATION METHOD OF WIDTH PREDICTION MODEL OF FINISHED ROLLED MATERIAL

Description

FIELD

The present invention relates to a width prediction method of a finished rolled material, a width control method of the finished rolled material, a manufacturing method of a hot-rolled steel sheet, and a generation method of a width prediction model of the finished rolled material in a hot rolling line.

BACKGROUND

In a hot rolling line, first, a slab which is a steel piece material is heated by a heating furnace, the width of the slab is adjusted by a width reduction pressing device (sizing press), and a semi-finished steel sheet (hereinafter, referred to as rough rolled material) called a rough bar having a sheet thickness of about 30 to 50 mm is manufactured by rough rolling using one or two or more rough rolling mills. Next, leading and trailing end portions of the rough rolled material is cut with a crop shear, and then the rough rolled material is finish-rolled with a finish rolling mill including 5 to 7 rolling stands capable of continuous rolling to manufacture a steel sheet (hereinafter, referred to as a finished rolled material) having a sheet thickness of about 1.0 to 25.0 mm. Finally, the finished rolled material in a high temperature state is cooled by a cooling device of a run-out table and then wound up by a coiler (winding machine) into a hot-rolled steel sheet. In the hot rolling line, since plastic deformation in a thickness direction and a width direction of the steel sheet is imparted in the width reduction pressing device, the rough rolling mill, and the finish rolling mill, the width of the steel sheet complicatedly varies in manufacturing processing of the hot-rolled steel sheet. On the other hand, the width accuracy of the hot-rolled steel sheet directly affects the product yield. Therefore, in the hot rolling line, the width of the rough rolled material at a stage before the rough rolling is completed and the rough rolled material is loaded into the finish rolling mill is controlled (rough width control), and the width of the steel sheet is controlled (finish width control) in the process of passing through the finish rolling mill.

In the hot rolling line, since the width of the steel sheet is changed due to various factors, various techniques for improving the width accuracy of the hot-rolled steel sheet have been proposed. For example, Patent Literature 1 discloses a method of controlling the width (hereinafter, referred to as a finish delivery-side width) of the finished rolled material. Specifically, in the method disclosed in Patent Literature 1, a width change amount of the steel sheet in the finish rolling mill is calculated, and an opening degree of an ejector installed on the entry side of the rough rolling mill and/or the finish rolling mill is controlled on the basis of a calculated value and a target value of the finish delivery-side width, thereby controlling the finish delivery-side width. In addition, Patent Literature 1 discloses that the width change amount of the steel sheet in the finish rolling mill is predicted using a prediction formula using the thickness of a steel sheet, a rolling reduction ratio, inter-rolling stand tension, a crown ratio change, a deformation resistance and a temperature of the steel sheet, and the inter-rolling stand passing time as parameters in each rolling stand. Furthermore, in the method described in Patent Literature 1, a prediction formula is calculated by dividing a region into three regions, a region in the vicinity of a roll bite entrance, a region inside a roll bite, and a region between the rolling stands.

In addition, Patent Literature 2 also discloses a method of controlling the finishing delivery-side width. In addition, Patent Literature 2 discloses that, when a prediction formula for predicting a width change amount of a steel sheet in a finish rolling mill is used, a different formula is applied as a prediction formula for a width change in the vicinity of a roll bite depending on whether a crown ratio change in each rolling stand is positive or negative. In addition, Patent Literature 3 discloses a method of correcting a target value of the width of the steel sheet on the basis of a deviation of an actual measurement value of the width of the steel sheet acquired at an initial stage of rolling from the target value when controlling the finish delivery-side width. That is, in the method disclosed in Patent Literature 3, performance data of the width change amount of the steel sheet at the time of finish rolling in the initial stage of rolling is acquired, and the target value of the width of the steel sheet is corrected on the basis of the performance data.

CITATION LIST

Patent Literature

• • Patent Literature 1: JP H05-285516 A
  • Patent Literature 2: JP H08-112609 A
  • Patent Literature 3: JP 2006-51512 A

Non Patent Literature

• • Non Patent Literature 1: “Gaussian Processes and Machine Learning”, authored by Daichi MOCHIHASHI and Shigeyuki OBA, published on Mar. 7, 2019, ISBN978-4-06-152926-7, by Kodansha

SUMMARY

Technical Problem

However, the prediction formula used in the method disclosed in Patent Literature 1 calculates a representative value of the width change amount of the steel sheet in the finish rolling mill, and does not predict the variation in the width change amount of the steel sheet. Therefore, according to the method disclosed in Patent Literature 1, it is inevitable that the variation occurs in the width change amount of the steel sheet due to factors such as a temperature estimation error of the steel sheet during finish rolling, and the finish delivery-side width becomes too small or too large. In addition, the method disclosed in Patent Literature 2 similarly calculates a representative value of the width change amount of the steel sheet in the finish rolling mill, and does not predict the variation in the width change amount of the steel sheet. Therefore, it is inevitable that the finish delivery-side width becomes too small or too large. On the other hand, the method disclosed in Patent Literature 3 is intended to specify the variation in the width change amount of the steel sheet in the finish rolling mill on the basis of actual measurement data acquired at the initial stage of rolling. However, since the width change amount of the steel sheet in the finish rolling mill varies depending on a change in operational conditions, there is room for improvement in predicting the variation in the width change amount of the steel sheet with high accuracy.

As described above, the finish width control in the related art intends to improve the accuracy of the finish delivery-side width by predicting the width change amount of the steel sheet using a strict physical model or specifying the variation in the width change amount of the steel sheet acquired from the actual value. However, it is inevitable that the variation occurs in the width change amount of the steel sheet in the finish rolling mill due to various causes. Therefore, the width of the steel sheet may be too small or too large in some cases, and it is inevitable that the width accuracy of the hot-rolled steel sheet is poor and the product yield is lowered.

The present invention has been made to solve the above problems, and an object thereof is to provide a width prediction method of a finished rolled material capable of predicting statistical information including variation in a width of the finished rolled material. In addition, another object of the present invention is to provide a width control method of a finished rolled material capable of accurately controlling the width in a longitudinal direction of the finished rolled material in consideration of the variation in the width of the finished rolled material. In addition, still another object of the present invention is to provide a manufacturing method of a hot-rolled steel sheet capable of improving the product yield of the hot-rolled steel sheet. In addition, still another object of the present invention is to provide a generation method of a width prediction model of a finished rolled material capable of generating the width prediction model for predicting statistical information including the variation in the width of the finished rolled material.

Solution to Problem

To solve the problem and achieve the object, a width prediction method of a finished rolled material according to the present invention is the width prediction method predicting a width of the finished rolled material in a hot rolling line including a heating furnace configured to heat a slab, a rough rolling mill configured to manufacture a rough rolled material by performing rough rolling on the heated slab, and a finish rolling mill configured to manufacture the finished rolled material by performing finish rolling on the rough rolled material. The width prediction method includes a prediction step of predicting statistical information of the width of the finished rolled material using a width prediction model trained by a Gaussian process regression method, the width prediction model for which an input data is data including a set value or an actual measurement value of a width of the rough rolled material and one or more operational parameters selected from operational parameters of the finish rolling mill, and an output data is the statistical information of the width of the finished rolled material.

Moreover, the width prediction model may include, as the input data, one or more parameters selected from attribute information of the slab.

Moreover, a width control method of a finished rolled material according to the present invention is the width control method including a setting step of predicting statistical information of a width of the finished rolled material using the width prediction method of the finished rolled material according to the present invention, and setting one or more operational parameters selected from operational parameters of the finish rolling mill such that a probability that the width of the finished rolled material falls below a target width becomes small, on a basis of the predicted statistical information.

Moreover, the statistical information of the width of the finished rolled material may include a mean value W_m and a standard deviation W_σ of the width of the finished rolled material, and the setting step may include a step of setting one or more operational parameters selected from the operational parameters of the finish rolling mill such that the target width W_t of the finished rolled material satisfies a relationship illustrated in following Expression (1).

W m → 2 . 5 ⁢ W σ ≦ W t ≦ W m - 1 . 5 ⁢ W σ ( 1 )

Moreover, a manufacturing method of a hot-rolled steel sheet according to the present invention is the manufacturing method including a step of manufacturing the hot-rolled steel sheet using the width control method of the finished rolled material according to present invention.

Moreover, a generation method of a width prediction model of a finished rolled material according to the present invention is the generation method generating a width prediction model of predicting a width of the finished rolled material in a hot rolling line including a heating furnace configured to heat a slab, a rough rolling mill configured to manufacture a rough rolled material by performing rough rolling on the heated slab, and a finish rolling mill configured to manufacture the finished rolled material by performing finish rolling on the rough rolled material. The generation method includes: a learning data acquisition step of acquiring a plurality of pieces of learning data including performance data of a set value or an actual measurement value of a width of the rough rolled material, one or more pieces of operational performance data selected from operational performance data of the finish rolling mill, and performance data of the width of the finished rolled material; and a step of generating the width prediction model using a Gaussian process regression method in which the performance data of the set value or the actual measurement value of the width of the rough rolled material and the one or more pieces of operational performance data selected from the operational performance data of the finish rolling mill are included as input performance data and statistical information of the width of the finished rolled material is output data, using the plurality of pieces of learning data acquired in the learning data acquisition step.

Advantageous Effects of Invention

With the width prediction method of the finished rolled material according to the present invention, it is possible to predict the statistical information including the variation in the width of the finished rolled material. In addition, with the width control method of the finished rolled material according to the present invention, it is possible to accurately control the width in the longitudinal direction of the finished rolled material in consideration of the variation in the width of the finished rolled material. In addition, with the manufacturing method of the hot-rolled steel sheet according to the present invention, it is possible to improve the product yield of the hot-rolled steel sheet. In addition, with the generation method of the width prediction model of the finished rolled material according to the present invention, it is possible to generate the width prediction model for predicting statistical information including the variation in the width of the finished rolled material.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram illustrating a configuration example of a hot rolling line to which the present invention is applied.

FIG. 2 is a schematic diagram illustrating a configuration example of a finish rolling mill illustrated in FIG. 1.

FIG. 3 is a schematic diagram illustrating a configuration example of one rolling stand constituting the finish rolling mill illustrated in FIG. 2.

FIG. 4 is a schematic diagram for describing an operation of a looper disposed between rolling stands of the finish rolling mill illustrated in FIG. 2.

FIG. 5 is a schematic diagram for describing an optical width measurement method.

FIG. 6 is a flowchart illustrating a flow of a model generation step according to an embodiment of the present invention.

FIG. 7 is a flowchart illustrating a flow of a prediction step according to an embodiment of the present invention.

FIG. 8 is a block diagram illustrating a configuration of a width prediction model generation unit according to an embodiment of the present invention.

FIG. 9 is a diagram for describing a setting method of a control target width in a width control method in the related art.

FIG. 10 is a block diagram illustrating a configuration of a width prediction unit according to an embodiment of the present invention.

FIG. 11 is a diagram illustrating a relationship between a probability density distribution of a finish delivery-side width predicted by a width prediction model and an aimed width.

FIG. 12 is a diagram for describing a setting method of a control target value of the finish width control in the present embodiment.

FIG. 13 is a diagram illustrating a relationship between a probability density distribution of a finish delivery-side width predicted by a width prediction model and an aimed width.

FIG. 14 is a diagram illustrating a relationship between a deviation of a finish delivery-side width from an aimed width and a cut-off amount of a steel sheet.

DESCRIPTION OF EMBODIMENTS

Hereinafter, a width prediction method of a finished rolled material, a width control method of a finished rolled material, a manufacturing method of a hot-rolled steel sheet, and a generation method of a width prediction model of a finished rolled material according to an embodiment of the present invention will be described in detail with reference to the drawings.

[Hot Rolling Line]

First, a configuration of a hot rolling line to which the present invention is applied will be described with reference to FIGS. 1 to 5.

FIG. 1 is a schematic diagram illustrating a configuration example of the hot rolling line to which the present invention is applied. As illustrated in FIG. 1, a hot rolling line 1 to which the present invention is applied includes a heating furnace 2, a descaling device 3, a width reduction pressing device 4, a rough rolling mill 5, a finish rolling mill 6, a cooling device 7, and a coiler (winding machine) 8. A cast slab (not illustrated) is loaded into the heating furnace 2, then heated to a predetermined set temperature, and extracted from the heating furnace 2 as a hot slab. The hot slab extracted from the heating furnace 2 is subjected to width reduction to a predetermined set width by the width reduction pressing device 4 after a primary scale formed on the surface is removed by the descaling device 3. The slab subjected to the width reduction is rolled to a predetermined thickness in the rough rolling mill 5 to become a rough rolled material, and is conveyed to the finish rolling mill 6. In the finish rolling mill 6, the rough rolled material is rolled to a product thickness by a continuous rolling mill including 5 to 7 rolling stands, to become a finished rolled material. The cooling device 7 is provided in a facility called a run-out table on the downstream side of the finish rolling mill 6, and the finished rolled material is cooled to a predetermined temperature and then wound into a coil shape by the coiler 8.

In addition, a plurality of width meters are installed as width measuring means in the middle of a conveyance step of the hot rolling line 1. In the example illustrated in FIG. 1, a rough delivery-side width meter 11 is installed on the delivery side of the rough rolling mill 5, and a finish delivery-side width meter 12 is installed on the delivery side of the finish rolling mill 6. In addition, a coiler entry width meter (coiler entry-side width meter) 13 that measures the width of the finished rolled material before winding is installed on the delivery side of the cooling device 7. In addition, on the entry side of the finish rolling mill 6, a finish entry-side width meter 14 for measuring the width of the rough rolled material is installed. However, unless means for applying plastic deformation to the rough rolled material is provided between the rough rolling mill 5 and the finish rolling mill 6, the width of the rough rolled material measured by the rough delivery-side width meter 11 and the width of the rough rolled material measured by the finish entry-side width meter 14 are the same. In the present embodiment, the width of the rough rolled material measured by the rough delivery-side width meter 11 may be referred to as a rough delivery-side width, the width of the finished rolled material measured by the finish delivery-side width meter 12 may be referred to as a finish delivery-side width, and the width of the steel sheet measured by the coiler entry width meter 13 may be referred to as a coiler entry width. In addition, the width of the rough rolled material measured by the finish entry-side width meter 14 is sometimes referred to as a finish entry-side width, but this may be regarded as the same as the rough delivery-side width.

The hot rolling line 1 includes a control controller (PLC) 90 that controls each device constituting the hot rolling line 1, a control computer (process computer) 91 that gives a control command to the control controller 90, and a host computer 92 that gives a manufacturing instruction to the hot rolling line 1. The width control of the steel sheet in the hot rolling line 1 is executed by the host computer 92 or the control computer 91 setting a control target value of the rough delivery-side width (rough control target width), a control target value of the finish delivery-side width (finish control target width), and a control target value of the coiler entry width (coiler entry control target width) on the basis of a manufacturing instruction from the host computer 92, and setting operational conditions of the rough rolling mill 5 and the finish rolling mill 6. Specifically, the host computer 92 or the control computer 91 sets a finish aimed width (hereinafter, sometimes simply referred to as an aimed width), which is a target width of the finished rolled material, in consideration of the width change amount of the steel sheet generated between the delivery side of the finish rolling mill 6 and the coiler entry width meter 13 on the basis of the coiler entry target width (coiler entry aimed width) determined from the product specification of the hot-rolled steel sheet. Furthermore, the host computer 92 or the control computer 91 sets the target width (rough aimed width) of the rough rolled material in consideration of the width change amount of the steel sheet in the finish rolling mill 6 on the basis of the set finish target width. In this case, the target value (rough control target width, finish control target width, coiler entry control target width) of the width control may be set by providing an extra width (margin) in advance with respect to the rough aimed width, the finish aimed width, and the coiler entry aimed width. Then, the host computer 92 or the control computer 91 sets rolling conditions in each pass of the rough rolling such that the rough delivery-side width matches the rough control target width. In addition, the host computer 92 or the control computer 91 sets the rolling conditions in each rolling stand of the finish rolling such that the finish delivery-side width matches the finish control target width. Furthermore, the host computer 92 or the control computer 91 may set the tension between the finish rolling mill 6 and the coiler 8 and a cooling condition of the cooling device 7 such that the coiler entry width matches the coiler entry control target width. In this case, in the finish rolling mill 6, dynamic width control may be executed while referring to actual measurement values of the rough delivery-side width and the finish delivery-side width. The control controller 90 has a function of collecting information acquired from various sensors (sheet thickness meter, thermometer, and the like) at a predetermined sampling cycle in addition to information acquired from the width meters installed in the hot rolling line 1, and of outputting the information to the control computer 91.

The width prediction method of the finished rolled material according to an embodiment of the present invention is a method of predicting the finish delivery-side width. In addition, the width control method of the finished rolled material according to an embodiment of the present invention is a method of controlling the width of the steel sheet such that the finish delivery-side width satisfies a predetermined relationship with respect to the finish aimed width.

[Finish Rolling Mill]

FIG. 2 is a schematic diagram illustrating a configuration example of the finish rolling mill 6 illustrated in FIG. 1. The rough rolled material is conveyed to the entrance of the finish rolling mill 6. As illustrated in FIG. 2, a crop shear 61 is disposed at the entrance of the finish rolling mill 6. The crop shear 61 is a device that cuts and removes a crop (an irregular-shaped portion of the leading and trailing end of the rough rolled material) formed at the leading and trailing end portion of the rough rolled material. As a result, the rough rolled material is shaped into a substantially rectangular planar shape to facilitate smooth biting into the finish rolling mill 6. A rough rolled material SA loaded into the finish rolling mill 6 is hereinafter simply referred to as a steel sheet SB. The finish rolling mill 6 illustrated in FIG. 2 includes seven rolling stands F1 to F7, but the number of rolling stands is not limited thereto. In general, the number of rolling stands of the finish rolling mill 6 is six to seven, and the finish rolling mill 6 may include five rolling stands. The finish rolling mill 6 takes a form of a hot tandem finish rolling mill in which the steel sheet SB reduced to a temperature set in accordance with the steel type and the like within a range of 800 to 1100° C. is simultaneously rolled by a plurality of rolling stands, but is simply referred to as a “finish rolling mill” for short.

FIGS. 3(a) and 3(b) are schematic diagrams illustrating a configuration example of one rolling stand constituting the finish rolling mill 6 illustrated in FIG. 2. As illustrated in FIGS. 3(a) and 3(b), the rolling stand has a structure including a pair of work rolls 62a and 62b positioned above and below a pass line of the steel sheet SB. The work rolls 62a and 62b are supported by back-up rolls 63a and 63b, respectively. A rolling load applied to the steel sheet SB is transmitted to a housing 65 via bearing portions (back-up roll chocks) 64a and 64b of the back-up rolls 63a and 63b. A load cell 66 as a load detector is disposed between the housing 65 and the back-up roll chock 64b, and a rolling load to be applied to the steel sheet SB can be measured by the load cell 66. In addition, the upper back-up roll chock 64a and the housing 65 are coupled via a reduction cylinder 67, and the reduction cylinder 67 can adjust the opening degree (roll gap) between the pair of work rolls 62a and 62b by adjusting the positions of the pair of work rolls 62a and 62b in an up-down direction.

The rolling stands F1 to F7 constituting the finish rolling mill 6 include a shape control actuator for controlling the profile (thickness distribution in the width direction of the steel sheet SB) and the flatness of the steel sheet SB. The shape control actuator is a mechanism for adjusting the roll gap distribution between the pair of work rolls 62a and 62b. A typical example of the shape control actuator is a work roll bender. The work roll bender includes a hydraulic device (not illustrated) that applies a force between bearing housings (work roll chocks) 68a and 68b at both end portions of each of the pair of work rolls 62a and 62b. The hydraulic device applies a force between the upper and lower work roll chocks 68a and 68b to apply a bending force to the pair of work rolls 62a and 62b, and applies flexural deformation to the pair of work rolls 62a and 62b to adjust the roll gap distribution. At this time, the force applied between the upper and lower work roll chocks 68a and 68b is referred to as a vender force. In addition, the rolling stands F1 to F7 are often provided with other shape control actuators as shape control actuators in addition to the work roll bender. For example, in the case of a pair cross mill, the roll gap distribution is adjusted by inclining (crossing) the lower work roll 62b and the lower back-up roll 63b in a horizontal plane with the upper work roll 62a and the upper backup roll 63a as one set. In this case, an angle formed by the upper and lower rolls is referred to as a cross angle, and the roll gap distribution is changed by changing the cross angle. In addition, the shape control actuator may use a work roll shift in which the pair of work rolls 62a and 62b is shifted in directions opposite to each other with respect to an axial direction. Furthermore, in a case where the rolling stand is a six-stage rolling mill, an intermediate roll shift in which upper and lower intermediate rolls are shifted in opposite directions to each other with respect to the axial direction of the roll is used. The shape control actuator provided in the rolling stand can adjust the width of the steel sheet SB by changing the crown ratio of the steel sheet SB by adjusting the distribution of the roll gap.

FIG. 4 is a schematic diagram for describing an operation of the looper disposed between the rolling stands F1 to F7 of the finish rolling mill 6 illustrated in FIG. 2. A looper 69 illustrated in FIG. 4 is a device for adjusting a balance between the conveyance speed of the steel sheet SB unloaded from the rolling stand Fi on the upstream side and the conveyance speed of the steel sheet SB loaded into the rolling stand Fi+1 on the downstream side. The looper 69 includes a looper roll 69a of which the distal end is in contact with the steel sheet SB. The looper 69 controls a looper angle Lθ and a looper height LH such that the inter-rolling stand tension applied to the steel sheet SB between the rolling stand Fi and the rolling stand Fi+1 falls within a predetermined range. In addition, the work roll peripheral speed of the rolling stand Fi on the upstream side is controlled such that the looper height LH falls within a predetermined range. In this case, the inter-rolling stand tension may be measured using a load detector disposed on the looper roll 69a. In addition, the inter-rolling stand tension may be estimated from the torque loaded on an electric motor for driving the looper 69. In any case, since the width of the steel sheet SB is changed depending on the inter-rolling stand tension, the inter-rolling stand tension applied to the steel sheet SB is measured between the rolling stands of the finish rolling mill 6.

[Width Meter]

Returning to FIG. 1. The width of the steel sheet in the hot rolling line 1 is measured by the rough delivery-side width meter 11, the finish delivery-side width meter 12, the coiler entry width meter 13, and the finish entry-side width meter 14. The optical width measurement methods are often used for these width meters. In the optical width measurement method, a light source is disposed below a pass line through which a steel sheet is conveyed, and an image sensor is disposed above the pass line, and the width of the steel sheet is measured on the basis of a shadow length of the steel sheet in the width direction caused by the steel sheet passing through a light beam emitted from the light source. In addition, some width meters measure the width by specifying the position of the end portions of the steel sheet in the width direction with cameras. FIGS. 5(a) and 5(b) are schematic diagrams illustrating a configuration example of the rough delivery-side width meter using cameras. In the example illustrated in FIG. 5(a), a set of cameras 16a and 16b provided in the rough delivery-side width meter captures an image of the steel sheet SB including the end portions of the steel sheet SB in the width direction. As the cameras 16a and 16b, CMOS or CCD sensors are used. Then, an image processing unit provided in the rough delivery-side width meter specifies the position of the end portions of the steel sheet SB in the width direction from the images captured by the cameras 16a and 16b, and calculates a width W of the steel sheet SB on the basis of an installation interval of the cameras 16a and 16b. Reference numeral 15 in the drawing denotes the pass line. However, since the width meter images the end portions of the steel sheet SB in the width direction from an oblique direction, a measurement error of the width is likely to occur when the steel sheet SB floats from the pass line 15. Therefore, the width meter is often provided with a function of correcting the measurement error of the width in response to the floating of the steel sheet SB from the pass line. Specifically, as illustrated in FIG. 5(b), in a case where the steel sheet SB is conveyed at the height of a floating amount H from the pass line 15, the measurement error of the width is corrected as follows. That is, first, a set of cameras 16a and 16b arranged in the width direction of the steel sheet SB specifies both end portions of the steel sheet SB in the width direction, and specifies a measurement value W1 of the width. Next, another set of cameras 16c and 16d arranged in the width direction of the steel sheet SB specifies both end portions of the steel sheet SB in the width direction, and specifies a measurement value W2 of the width. Then, on the basis of a positional relationship of the two sets of cameras (in the example illustrated in FIG. 5(b), an interval D between the cameras 16a and 16b in the width direction and an interval L between the camera 16a (16b) and the camera 16c (16d) in the width direction), the actual width W of the steel sheet SB is calculated by the following Expression (2) and taken as the measurement value of the width of the steel sheet SB.

W = ( D + 2 ⁢ L ) ⁢ W ⁢ 1 - DW ⁢ 2 ( W ⁢ 1 - W ⁢ 2 + 2 ⁢ L ) ( 2 )

However, as another width measurement method, a method of emitting laser light in the width direction of the steel sheet, receiving reflected light from an end surface of the steel sheet, and measuring the width of the steel sheet on the basis of the distance to both end surfaces of the steel sheet may be used. Some width meters have a thermal expansion correction function of converting the width into a width of the steel sheet after cooling on the basis of the temperature of the steel sheet. Since the width of the steel sheet is measured using the width meter in the process of conveying the steel sheet, the width measurement value of the steel sheet obtained by the width meter is time-series numerical information corresponding to the sampling pitch of the width meter. In addition, information on the conveyance speed at which the steel sheet passes through the position of the width meter is used to be converted into a relationship between the position of the steel sheet in a longitudinal direction and the actual value of the width of the steel sheet. Then, the control computer 91 calculates a representative value of the width of the steel sheet on the basis of the acquired actual measurement value of the width of the steel sheet. As the representative value of the width of the steel sheet, a mean value (mean width) of the width of the steel sheet in the longitudinal direction of the steel sheet, an actual measurement value (steady width) of the width of the steel sheet in a steady portion excluding the leading and trailing end portions of the steel sheet, an actual measurement value (leading end width) of the width of the steel sheet in the leading end portion of the steel sheet, an actual measurement value (trailing end width) of the width of the steel sheet in the trailing end portion of the steel sheet, and the like are used. In addition, the minimum value (minimum width), the maximum value (maximum width), and the like of the width of the steel sheet in the longitudinal direction of the steel sheet may be calculated. The actual measurement value of the width of the steel sheet measured by the width meter may be represented by a deviation from a target width set in advance.

[Gaussian Process Regression]

The width prediction method of the finished rolled material according to an embodiment of the present invention predicts the finish delivery-side width in the hot rolling line 1 described above. The width prediction method of the finished rolled material according to an embodiment of the present invention uses a width prediction model trained by a Gaussian process regression method in which a set value or an actual measurement value of the width of the rough rolled material and one or more operational parameters selected from the operational parameters of the finish rolling mill 6 are included as input data and statistical information of the finish delivery-side width is output data. In the following, a Gaussian process regression method applied to the width prediction method of the finished rolled material according to an embodiment of the present invention will be described.

The Gaussian process regression is also called a Gaussian process regression, a Gaussian process, or the like, and is a type of nonlinear regression model that estimates a function mapping an input variable to an output variable. The output is a probability distribution, and the use of the Gaussian distribution specified by two parameters of the mean and the variance is called a Gaussian process. The probability distribution is obtained using a Bayesian estimation method, and the reliability and uncertainty of the estimation can be expressed. For example, an input variable in a case where m variables are selected as inputs of the width prediction model is represented by an input vector x. In addition, an output variable associated with the input vector x as learning data is set to y. Hereinafter, a method of obtaining statistical information y* of the finish delivery-side width with respect to a new input vector x* by the Gaussian process regression method using n pieces of learning data x⁽¹⁾ to x⁽ⁿ⁾ and y⁽¹⁾ to y⁽ⁿ⁾ will be specifically described. Since the m variables constituting the input vector x represent different physical quantities, the m variables may be standardized (normalized) in advance. Specifically, for each of the m variables, a mean value and a standard deviation may be calculated from the n pieces of learning data, and each variable may be standardized using the calculated mean value and standard deviation. This is because, by standardizing m variables in advance, learning of hyperparameters to be described later is made efficient. In this case, in order to convert m variables into physical quantities, inverse conversion may be performed using the calculated mean value and standard deviation.

In the Gaussian process regression, a probability model is used which estimates a function f(x) mapping the input variable x to the output variable y, with Gaussian noise added. For example, the probability model is represented as the following Expression (3). In this case, it is assumed that the function f(x) follows a multivariate Gaussian distribution. In addition, it is assumed that the Gaussian noise ε⁽ⁱ⁾ follows the Gaussian distribution having the mean of zero and the variance of σ_i⁽ⁱ⁾². However, the Gaussian noise ε⁽ⁱ⁾ may be a value depending on the n pieces of learning data x⁽¹⁾ to x⁽ⁿ⁾, or may be constant noise regardless of the n pieces of learning data x⁽¹⁾ to x⁽ⁿ⁾.

y ( i ) = f ⁡ ( x ( i ) ) + ϵ ( i ) ( 3 )

The Gaussian distribution refers to a distribution in which the probability density N is represented by the following Expression (4). In Expression (4), μ represents a mean value, and σ represents a standard deviation (σ² is variance). That is, the Gaussian distribution is a probability density specified by the mean value μ and the standard deviation σ or the variance σ². The Gaussian process regression uses a multivariate normal distribution obtained by extending such a Gaussian distribution in multiple dimensions.

N ⁡ ( μ , σ 2 ) = 1 2 ⁢ πσ 2 · exp ⁡ ( - ( x - μ ) 2 2 ⁢ σ 2 ) ( 4 )

In the Gaussian process regression, a covariance matrix is represented by a kernel function with a mean function (mean vector) representing a multivariate Gaussian distribution as a constant (for example, zero). The kernel function is a function for calculating data similarity. The kernel function is represented as k(x⁽ⁱ⁾, x^(j)) using input vectors x⁽ⁱ⁾ and x^(j) as arguments, and outputs the similarity between the input vector x⁽ⁱ⁾ and the input vector x^(j). As the kernel function, a known kernel function such as a white kernel, a linear kernel, a polynomial kernel, a Gaussian kernel, or a Matern kernel can be used. Some kernel functions are represented as the following Expressions (5) to (7) using the parameter θ. Expression (5) represents a linear kernel, Expression (6) represents a second-order polynomial kernel, and Expression (7) represents a Gaussian kernel.

k ⁡ ( x ( i ) , x ( j ) ) = θ · x ( i ) · x ( j ) ⁢ T ( 5 ) k ⁡ ( x ( i ) , x ( j ) ) = ( 1 + θ · x ( i ) · x ( j ) ⁢ T ) 2 ( 6 ) k ⁡ ( x ( i ) , x ( j ) ) = exp ⁡ ( - ( x ( i ) - x ( j ) ) 2 / θ ) ( 7 )

According to the above assumption, the function f(x) mapping the input variable x to the output variable y is represented as the following Expression (8) using the probability density N.

[ y ( 1 ) ⋮ y ( n ) ] = [ f ( 1 ) ⋮ f ( n ) ] + [ σ e ( 1 ) 2 ⋮ σ e ( n ) 2 ] = N ⁡ ( [ 0 ⋮ 0 ] , [ k ⁢ ( x ( 1 ) , x ( 1 ) ) … k ⁢ ( x ( 1 ) , x ( n ) ) ⋮ ⋱ ⋮ k ⁢ ( x ( n ) , x ( 1 ) ) … k ⁢ ( x ( n ) , x ( n ) ) ] ) + [ σ e ( 1 ) 2 ⋮ σ e ( n ) 2 ] ( 8 )

In this case, in a case where the Gaussian noise has a constant value σ_e² regardless of the learning data, when the covariance matrix K_n specified by the kernel function and the covariance matrix Σ_n including the Gaussian noise are defined by the following Expressions (9) and (10), Expression (8) is represented as the following Expression (11) or (12). Here, I represents an identity matrix.

K n = [ k ⁢ ( x ( 1 ) , x ( 1 ) ) … k ⁢ ( x ( 1 ) , x ( n ) ) ⋮ ⋱ ⋮ k ⁢ ( x ( n ) , x ( 1 ) ) … k ⁢ ( x ( n ) , x ( n ) ) ] ( 9 ) Σ n = [ k ⁢ ( x ( 1 ) , x ( 1 ) ) + σ e 2 … k ⁢ ( x ( 1 ) , x ( n ) ) ⋮ ⋱ ⋮ k ⁢ ( x ( n ) , x ( 1 ) ) … k ⁢ ( x ( n ) , x ( n ) ) + σ e 2 ] ( 10 ) y ( i ) = N ⁡ ( 0 , K n + σ e 2 ⁢ I ) ( 11 ) y ( i ) = N ⁡ ( 0 , Σ n ) ( 12 )

The covariance matrixes K_n and Σ_n included on the right sides of Expressions (11) and (12) include learning data x⁽¹⁾ to x⁽ⁿ⁾ as inputs, and the left sides of Expressions (11) and (12) include learning data y⁽¹⁾ to y⁽ⁿ⁾ as outputs. Therefore, the hyperparameters (parameter θ and Gaussian noise σ_e²) included in the kernel function may be determined so that the relationship shown in Expression (11) or Expression (12) is established. As a method of determining the hyperparameter, a method selected from known methods may be used. For example, the hyperparameter may be calculated by calculating a likelihood function of the learning data and maximizing the log likelihood represented by the log of the calculated likelihood function. In this case, as a calculation method of maximizing the log likelihood, an optimization method such as a Monte Carlo method or a conjugate gradient method can be used. In addition, a method such as a cross verification method or peripheral likelihood maximization may be used.

Next, a method will be described which estimates the statistical information y* of the finish delivery-side width with respect to the new input vector x* using the function f(x) in which the hyperparameter of the kernel function is determined. The estimated value for the unknown input vector x* not included in the learning data can be represented as the following Expression (13) by applying Bayesian estimation. In this case, the vector of the newly specified kernel function k* is defined as the following Expression (14).

[ y ( 1 ) ⋮ y ( n ) y * ] = N ⁡ ( [ 0 ⋮ 0 0 ] , [ k ⁢ ( x ( 1 ) , x ( 1 ) ) + σ e 2 … k ⁢ ( x ( 1 ) , x ( n ) ) k ⁢ ( x ( 1 ) , x * ) ⋮ ⋱ ⋮ ⋮ k ⁢ ( x ( n ) , x ( 1 ) ) … k ⁢ ( x ( n ) , x ( n ) ) + σ e 2 k ⁢ ( x ( n ) , x * ) k ⁢ ( x * , x ( 1 ) ) … k ⁢ ( x * , x ( n ) ) k ⁢ ( x * , x * ) + σ e 2 ] ) ( 13 ) k * = [ k ⁢ ( x ( 1 ) , x * ) ⋮ k ⁢ ( x ( n ) , x * ) ] ( 14 )

As a result, Expression (13) can be represented as the following Expression (15). Then, the statistical information for the input vector x* can be calculated by the following Expressions (16) and (17) with the mean value as W_m and the variance as W_σ. For details of the Gaussian process regression method, a known document (for example, Non Patent Literature 1) or the like may be referred to.

[ y ( 1 ) ⋮ y ( n ) y * ] = N ( [ 0 ⋮ 0 0 ] , [ Σ n k * k * T k ⁢ ( x * , x * ) + σ e 2 ] ( 15 ) W m ( x * ) = k * · Σ n - 1 · [ y ( 1 ) ⋮ y ( n ) ] ( 16 ) W σ ( x * ) = k ⁡ ( x * , x * ) + σ e 2 - k * · Σ n - 1 · k * T ( 17 )

In the present embodiment, a step of specifying the hyperparameter so as to represent the relationship of the above Expression (11) or Expression (12) is referred to as a model generation step. Specifically, in the model generation step, as illustrated in FIG. 6, first, n pieces of learning data x⁽¹⁾ to x⁽ⁿ⁾ and y⁽¹⁾ to y⁽ⁿ⁾ are acquired from a data set accumulated in a database or the like (step S1). Next, a kernel function used for machine learning is selected from, for example, Expressions (5) to (7) (step S2). Next, a Gaussian distribution having a mean value of zero and a variance of σ_e² is set as the Gaussian noise ε⁽ⁱ⁾ (step S3). Next, covariance matrixes K_n and Σ_n specified by the kernel function are calculated using Expressions (9) and (10) (step S4). Then, the parameter θ and the Gaussian noise cy are determined as hyperparameters by a learning method using the likelihood function using Expressions (11) and (12) representing the relationship between the input and output of the learning data (step S5). The kernel function representing the input/output relationship of the learning data is specified by the hyperparameter determined in this manner. The determined hyperparameter may be stored in a storage device of a computer that executes the model generation step. On the other hand, a step of calculating the mean value W_m and the standard deviation W_σ as statistical information for the input vector x* using the hyperparameter determined by the model generation step is referred to as a prediction step. Specifically, in the prediction step, as illustrated in FIG. 7, first, a new input vector x* is acquired (step S11). Next, the hyperparameter stored in the storage device of the computer that executes the model generation step is acquired, and the kernel function k* for the new input vector x* is specified using Expression (14) (step S12). Then, a prediction value for the input vector x* is calculated as the mean value W_m and the standard deviation W_σ using the relationships illustrated in Expressions (16) and (17) (step S13).

[Generation Method of Width Prediction Model]

Next, an embodiment to which the above-described Gaussian process regression method is applied will be described as a generation method of a width prediction model of a finished rolled material according to an embodiment of the present invention.

FIG. 8 is a block diagram illustrating a configuration of a width prediction model generation unit according to an embodiment of the present invention. As illustrated in FIG. 8, a width prediction model generation unit 100 according to the present embodiment includes a database unit 101 and a machine learning unit 102. In the database unit 101, a set value or an actual value of the rough delivery-side width, one or more pieces of operational performance data selected from the operational performance data of the finish rolling mill 6, and performance data of the finish delivery-side width are accumulated. The database unit 101 may accumulate one or more pieces of operational performance data selected from the operational performance data of attribute information of the slab as necessary. Specific performance data accumulated in the database unit 101 will be described later.

The performance data accumulated in the database unit 101 can be appropriately acquired from the control controller 90, the control computer 91, or the host computer 92. In addition, a data acquisition unit 103 may be provided to collect the performance data, and the performance data may be temporarily stored in the data acquisition unit 103, and then accumulated in the database unit 101 after a data set in which a plurality of types of performance data are associated is generated. Since the data accumulated in the database unit 101 may be acquired at different timings, a data set having a correspondence relationship with one another can be easily configured by associating a plurality of types of performance data in the data acquisition unit 103. For the data set accumulated in the database unit 101, at least one piece of performance data is acquired for one steel sheet manufactured from one slab. For example, in a case where the mean width of the finished rolled material is used as the performance data of the finish delivery-side width, the operational performance data of the finish rolling mill 6 may be represented using the representative value as the performance data. In this case, as the width data of the finished rolled material, a representative value for the finished rolled material may be used, but a set value or an actual measurement value of the width at a plurality of positions along the longitudinal direction of the finished rolled material may be used. For the performance data of the attribute information of the slab, a representative value for one steel sheet may be used as the performance data.

On the other hand, a plurality of data sets for one steel sheet manufactured from one slab may be generated in the data acquisition unit 103, and the plurality of data sets may be accumulated in the database unit 101. For example, in a case where the performance data related to the width at three points of the leading end portion, the steady portion, and the trailing end portion of the finished rolled material is acquired as the performance data of the finish delivery-side width, for the operational performance data of the finish rolling mill 6, the operational performance data acquired at each of the leading end portion, the steady portion, and the trailing end portion of the finished rolled material may be associated with the performance data of the finish delivery-side width at the corresponding position. However, for the performance data specified regardless of the position in the longitudinal direction of the steel sheet, such as the performance data of the attribute information of the slab, the performance data of the same attribute information is associated with the performance data of the finish delivery-side width at the leading end portion, the steady portion, and the trailing end portion of the steel sheet.

Furthermore, the data acquisition unit 103 may acquire the performance data of the finish delivery-side width for each position divided in the longitudinal direction with respect to one steel sheet, and the operational performance data acquired for each position in the longitudinal direction of the steel sheet may be accumulated in the database unit 101 in association with the performance data of the finish delivery-side width measured at each position. That is, the number of divisions in the longitudinal direction of the steel sheet is set to, for example, about 20 to 200, and the performance data of the finish delivery-side width in each divided section is associated with the operational performance data corresponding to each position. In this case, although the length of the steel sheet SB finish-rolled by the finish rolling mill 6 is changed for each rough rolling pass, in a case where the operational performance data at the position corresponding to the division of in the longitudinal direction of the steel sheet SB is acquired, the data acquisition unit 103 can configure the data set corresponding to each division section. In a case where data sets corresponding to a plurality of positions divided in the longitudinal direction of the steel sheet are accumulated in the database unit 101, the machine learning unit 102 can also generate a width prediction model different for each position in the longitudinal direction of the steel sheet.

The width prediction model generation unit 100 can be provided in the control computer 91 for controlling the manufacturing of the steel sheet by the hot rolling line 1. In addition, the width prediction model generation unit 100 may be provided in the host computer 92 that gives a manufacturing instruction to the control computer 91, or may be provided in an independent computer that can communicate with other devices. In addition, the machine learning unit 102 may be configured in a device separate from the database unit 101 by using a device capable of receiving the data set accumulated in the database unit 101. In the database unit 101, 100 or more data sets are accumulated. Preferably, 10,000 or more data sets, more preferably 100,000 or more data sets may be accumulated in the database unit 101. Screening may be performed on the data accumulated in the database unit 101 as necessary.

The machine learning unit 102 generates a width prediction model M by machine learning by the Gaussian process regression method using the data set accumulated in the database unit 101. The learning data used by the machine learning unit 102 is a plurality of data sets including performance data of the set value or the actual value of the rough delivery-side width, one or more pieces of operational performance data selected from the operational performance data of the finish rolling mill 6, and performance data of the finish delivery-side width that are accumulated in the database unit 101. Using the learning data, the machine learning unit 102 generates the width prediction model M by executing machine learning by the Gaussian process regression method in which the performance data of the set value or the actual value of the rough delivery-side width and one or more pieces of operational performance data selected from the operational performance data of the finish rolling mill 6 are included as input performance data and the statistical information of the finish delivery-side width is output data. In addition, the machine learning unit 102 may generate the width prediction model M by executing the machine learning by the Gaussian process regression method using the performance data of the attribute information of a slab SA as the input performance data by using the data set accumulated in the database unit 101.

The machine learning in this case refers to specifying the hyperparameter applied to the Gaussian process regression by the steps illustrated in FIG. 6. In addition, the width prediction model M refers to the hyperparameter specified in this manner. This is because the input/output relationship of the learning data is specified by specifying the hyperparameter, and the statistical information of the finish delivery-side width with respect to the unknown input can be predicted. In addition, in the present embodiment, the statistical information of the finish delivery-side width to be the output of the width prediction model M trained by the Gaussian process regression includes a prediction result of the mean value of the width of the finished rolled material and the standard deviation or variance which is an index representing the variation thereof. As a result, the variation can be predicted together with the mean value of the finish delivery-side width.

On the other hand, in the related art, for example, as disclosed in Patent Literatures 1 and 2, the mean value or the representative value of the width change amount of the steel sheet in the finish delivery-side width and the finish rolling mill is predicted by using the prediction formula that predicts the width change amount of the steel sheet in the finish rolling, but the information regarding the variation thereof cannot be obtained. Therefore, it is necessary to set a target value of the width of the steel sheet by adding a preset extra width (margin). Specifically, in the width control method in the related art, as illustrated in FIG. 9, an extra width (margin) W_r is set in advance with respect to the aimed width W_t, and the sum of the aimed width W_t and the extra width W_r is set as the control target width W_c of the finish delivery-side width. The reason for setting the extra width W_r is to prevent the finish delivery-side width from falling below the aimed width W_t since a certain variation occurs in the finish delivery-side width. When the finish delivery-side width falls below the aimed width W_t, the width of the steel sheet after hot rolling may fall below the product target width, and the product cannot be obtained due to the insufficient width. Therefore, the manufactured hot-rolled steel sheet may be scrapped or a shipping destination of a product may be changed, resulting in a decrease in product yield, a delay in delivery, and the like. On the other hand, when the extra width W_r to be set is too large, the width of the steel sheet after hot rolling becomes too large as compared with the product target width, and thus it is necessary to perform edge trimming (trimming) of the steel sheet in order to obtain a product, which reduces the product yield. That is, when an attempt is made to prevent the occurrence of the width insufficiency as the hot-rolled steel sheet, the finish delivery-side width becomes too large, and when an attempt is made to suppress a decrease in yield due to the edge trimming, the width insufficiency easily occurs. Therefore, in the technique in the related art, the performance data of the finish delivery-side width and the width change amount in the finish rolling mill 6 is collected for each classification of the thickness and the width of the hot-rolled steel sheet, an extra width is set in advance according to the variation, and a person in charge of the factory periodically monitors whether the setting of the extra width is appropriate.

On the other hand, according to the present embodiment, since the mean value and the statistical variation in the finish delivery-side width are predicted according to the operational condition of the hot rolling line to be input, it is possible to set an appropriate extra width according to the operational condition for each steel sheet instead of each classification of the thickness and the width of the hot-rolled steel sheet as in the technique in the related art. This makes it possible to suppress a decrease in product yield due to the width insufficiency or the width excess of the hot-rolled steel sheet caused by the variation in the finish delivery-side width.

[Attribute Information of Slab]

The attribute information of the slab that can be used for input of the width prediction model M refers to information regarding a slab dimension that affects the width change of the steel sheet in the finish rolling mill 6 and information regarding the composition of the slab. The information regarding the slab dimension is information regarding the thickness, width, length, and weight of the slab. The information regarding the composition of the slab is information regarding the content of the component contained in the slab, and examples thereof include the C content, the Si content, the Mn content, the P content, the S content, the Nb content, the Ti content, the Cu content, the Ni content, the Mo content, and the B content of the slab. The information regarding the slab dimension affects a temperature change of the steel sheet in the hot rolling line 1, and thus affects the variation in the finish delivery-side width. In addition, the information regarding the composition of the slab affects the deformation resistance of the steel sheet and the composition and thickness of an oxide film generated on the surface of the steel sheet. As a result, the frictional force at an interface between the rolling roll and the steel sheet is affected, and the deformation state of the steel sheet is changed, so that the variation in the finish delivery-side width is affected. Furthermore, the information regarding the composition of the slab affects the behavior of short-time creep deformation between rolling stands of the finish rolling mill 6. As a result, the width shrinkage in the finish rolling mill 6 is affected, and the variation in the finish delivery-side width is affected.

[Width Data of Rough Rolled Material]

The width data of the rough rolled material (the set value or the actual measurement value of the width of the rough rolled material) used for the input of the width prediction model M is a set value or an actual measurement value regarding the width of the rough rolled material to be loaded in the finish rolling mill 6. As the set value regarding the width of the rough rolled material, a representative value regarding the width of the rough rolled material used in the setting calculation for the control computer 91 to set the operational condition of the rough rolling mill 5 or the finish rolling mill 6 may be used. In addition, in a case where the control computer 91 sets the target width and the control target width of the width of the rough rolled material on the delivery side of the rough rolling mill 5 at the time of performing the rough rolling, the target width and the control target width can be used as the width data of the rough rolled material. In addition, the control computer 91 performs setting calculation using the width of the rough rolled material on the entry side of the finish rolling mill 6 before performing the finish rolling, and the setting value of the finish entry-side width used at this time may be the width data of the rough rolled material. On the other hand, as the actual measurement value regarding the width of the rough rolled material, an actual value of the rough delivery-side width measured by the rough delivery-side width meter 11 can be used. In addition, an actual value of the finish entry-side width measured by the finish entry-side width meter 14 can be used. The actual measurement values of the width of the rough rolled material measured by the rough delivery-side width meter 11 and the finish entry-side width meter 14 are sent from the control controller 90 to the control computer 91, so that these values can be acquired from the control computer 91 using the data acquisition unit 103.

[Operational Parameter of Finish Rolling Mill]

The operational parameters of the finish rolling mill 6 used for the input of the width prediction model M mean rolling operational conditions that affect the width of the steel sheet in an arbitrary rolling stand of the finish rolling mill 6. As the operational parameters of the finish rolling mill 6, operational parameters that affect the width of the steel sheet in three regions of a region in the vicinity of the roll bite entrance, a region inside the roll bite, and a region between the rolling stands corresponding to each rolling stand of the finish rolling mill 6 can be used. Specifically, the thickness of the steel sheet, the rolling reduction ratio, the inter-rolling stand tension, the crown ratio change, the deformation resistance and the temperature of the steel sheet in each rolling stand may be used. In addition, the rolling load, the roll opening degree, and the work roll diameter of each rolling stand, which indirectly affect the thickness and temperature of the steel sheet in each rolling stand, may be used as the operational parameters. Furthermore, a set value or an actual value of the shape control actuator that indirectly affects the crown ratio change of the steel sheet in each rolling stand may be used. For example, it is possible to use a set value or an actual value of an actuator for controlling the profile of the steel sheet by changing the deflection of the work roll, such as a vender force of a work roll bender, a cross angle in a pair cross mill, and an intermediate roll shift amount in a six-stage rolling mill. As the operational parameters of the finish rolling mill 6, in addition to these, operational parameters regarding the speed of the steel sheet, such as a rolling speed, an acceleration rate, a rolling time, a peripheral speed of a work roll of each rolling stand, and an inter-rolling stand passing time, may be used. This is because the temperature change and the deformation resistance of the steel sheet are affected, and thus the width change amount of the steel sheet is affected. In addition, this is because short-time creep deformation of the steel sheet is affected, and thus the width shrinkage between rolling stands is affected. Furthermore, as the operational parameters of the finish rolling mill 6, a rolling length, a use time, and the like after the work rolls used for each rolling stand are rearranged may be used. This is because the frictional state between the work roll and the steel sheet is changed as the surface state of the work roll is changed over time, and the width widening at the time of rolling is affected.

[Width Prediction Method of Finished Rolled Material]

The width prediction method of the finished rolled material according to an embodiment of the present invention includes a prediction step of predicting statistical information of the finish delivery-side width using the width prediction model M generated as described above. The width prediction unit that executes the prediction step can be provided in the control computer 91 for controlling the hot rolling line 1. In addition, the width prediction unit may be provided in the host computer 92 that gives a manufacturing instruction to the control computer 91, or may be provided in an independent computer that can communicate with other devices. Hereinafter, the operation of the width prediction unit according to an embodiment of the present invention will be described with reference to FIG. 10.

The operation of a width prediction unit 110 illustrated in FIG. 10 is executed before the finish delivery-side width of the steel sheet manufactured in the hot rolling line 1 is measured by the finish delivery-side width meter 12. The operation of the width prediction unit 110 can be executed, for example, in a stage when the steel sheet as a prediction target is loaded into the heating furnace 2 as a slab or in a stage when the steel sheet as a prediction target is extracted from the heating furnace 2. In a stage when the slab is loaded into the heating furnace 2, information regarding the slab dimension and the composition of the slab is specified by the host computer 92 as the attribute information of the slab. In addition, this is also because, at the stage where the slab is loaded into the heating furnace 2, manufacturing specifications of the hot-rolled steel sheet are set in advance, and standard operational parameters corresponding thereto are specified. Therefore, the prediction step can be executed by using the performance data of the attribute information of the slab and the set values of other operational parameters specified as standard operational parameters corresponding to the manufacturing specifications as inputs. In addition, the prediction step can also be performed, for example, in the middle of the rolling pass of the rough rolled material by the rough rolling mill 5. Since the rough width control in the rough rolling mill 5 is executed during the rough rolling, and the target width and the control target width for the rough delivery-side width are set, these set values can be used for the input of the width prediction model M.

Furthermore, the prediction step can be executed before the rough rolled material is loaded into the finish rolling mill 6 after the rough rolling is ended. When the rough rolling is ended, actual measurement values of the width of the rough rolled material can be acquired, and these actual values can be used for input of the width prediction model M. In addition, the rough delivery-side width is measured by the rough delivery-side width meter 11 and the finish entry-side width meter 14, so that the control computer 91 executes setting calculation of the finish rolling mill 6 on the basis of the actual measurement value of the rough delivery-side width, and the operational condition of the finish rolling mill 6 is set. Therefore, the operational parameters of the finish rolling mill 6 set by the setting calculation can be used for the input of the width prediction model M. The prediction step can be executed as needed after the leading end portion of the rough rolled material is loaded into the finish rolling mill 6 and before the trailing end portion of the rough rolled material passes through the finish rolling mill 6. In this case, since the actual value of the operational parameter of the finish rolling mill 6 at the present time can be acquired, the operational parameter of the finish rolling mill at the present time can be used for the input of the width prediction model M. As a result, it is possible to predict the finish delivery-side width at the time when the rough rolled material loaded into the rolling stand F1 of the finish rolling mill 6 is unloaded from the rolling stand F7.

As described above, an input data acquisition unit 111 of the width prediction unit 110 illustrated in FIG. 10 acquires the actual value or the set value of the operational parameter of the hot rolling line 1 held by the control computer 91 or the host computer 92. Then, the width prediction unit 110 inputs the input data acquired by the input data acquisition unit 111 to a prediction unit 112. The prediction unit 112 acquires the hyperparameter determined by the width prediction model generation unit 100, calculates the kernel function for the input data (new input vector) as illustrated in FIG. 7, and calculates statistical information of the finish delivery-side width as the output data. As described above, since the operation of the width prediction unit 110 can be executed as needed until the trailing end portion of the steel sheet passes through the finish rolling mill 6, the operation may be executed a plurality of times in the process of manufacturing one steel sheet. The statistical information of the finish delivery-side width output as described above may be displayed on a monitor or the like connected to the width prediction unit 110. The operational parameter of the finish rolling mill 6 is reset on the basis of the output display of the statistical information of the finish delivery-side width, and the occurrence of the width defect of the hot-rolled steel sheet can be suppressed.

[Width Control Method of Finished Rolled Material]

The width control method of the finished rolled material according to an embodiment of the present invention resets one or more operational parameters selected from the operational parameters of the finish rolling mill 6 on the basis of the statistical information of the finish delivery-side width predicted as described above, such that the probability that the finish delivery-side width falls below the target width (aimed width) W_t of the finished rolled material becomes small. In the width prediction method of the finished rolled material, the statistical information of the finish delivery-side width, which is the output of the width prediction model M, is specified as, for example, the mean value W_m of the finish delivery-side width and the standard deviation W_σ. In this case, the finish delivery-side width W is predicted to follow the probability density distribution g(W) illustrated in the following Expression (18).

ℊ ⁡ ( W ) = 1 2 ⁢ π ⁢ W σ 2 · exp ⁡ ( - ( W - W m ) 2 2 ⁢ W σ 2 ) ( 18 )

FIG. 11 is an example schematically illustrating the probability density distribution g(W) of the finish delivery-side width predicted by the width prediction model M together with the aimed width W_t. In FIG. 11, it is predicted that the finish delivery-side width W becomes smaller than the aimed width W_t with a high probability, from the fact that the mean value W_m of the finish delivery-side width W predicted by the width prediction model M is smaller than the aimed width W_t and from the variation in the finish delivery-side width W. In this case, it is predicted that the finish delivery-side width W becomes insufficient with a high probability from the operational conditions of the hot rolling line 1 set at the present time. Therefore, in the present embodiment, one or more operational parameters selected from the operational parameters of the finish rolling mill 6 are reset such that the probability that the finish delivery-side width W falls below the aimed width W_t becomes small. Specifically, the operational parameters of the finish rolling mill 6 are corrected such that the distribution of the probability density distribution g(W) indicated by the solid line in FIG. 11 becomes the probability density distribution indicated by the broken line. In this case, by executing the prediction step of predicting the statistical information of the finish delivery-side width W before the rough rolled material is loaded into the finish rolling mill 6, the control computer 91 executes the setting calculation again using the corrected operational parameters of the finish rolling mill 6. As a result, the operational parameters of the finish rolling mill 6 are set such that the probability that the finish delivery-side width W falls below the aimed width W_t becomes small. The operational parameters to be reset are preferably selected from the operational parameters used for the input of the width prediction model M. This is because, in FIG. 11, the statistical information of the finish delivery-side width W is output again using the reset operational parameters of the finish rolling mill 6 as the input of the width prediction model M, and whether or not the probability that the finish delivery-side width W falls below the aimed width W_t becomes small as indicated by the broken line in FIG. 11 is checked, whereby it is possible to determine whether or not the proper operational condition is reset.

On the other hand, as illustrated in FIG. 12, in a case where the probability that the finish delivery-side width W falls below the aimed width W_t is predicted to be higher than the probability density distribution g(W) of the finish delivery-side width predicted by the width prediction model M, the control target value W_c of the finish width control may be set such that the probability that the finish delivery-side width W falls below the aimed width W_t becomes small. As a result, the finish width control of the hot rolling line 1 is executed using the set control target value W_c, and even in a case where there is the variation in the finish delivery-side width W, the probability that the width becomes insufficient with respect to the aimed width W_t can be reduced. Furthermore, one or more operational parameters selected from the operational parameters of the finish rolling mill 6 are preferably reset such that the aimed width W_t satisfies the following Expression (1).

W m - 2.5 W σ ≦ W t ≦ W m - 1 . 5 ⁢ W σ ( 1 )

FIG. 13 is a schematic diagram illustrating a relationship between the probability density distribution g(W) of the finish delivery-side width W predicted by the width prediction model M and the aimed width W_t. Expression (1) above indicates that the aimed width W_t falls within a range of W_m−2.5W_σ and W_m−1.5W_σ, specified by the mean width W_m of the finish delivery-side width W output from the width prediction model M and the standard deviation W_σ. In this case, one or more operational parameters selected from the operational parameters of the finish rolling mill 6 may be reset such that the probability density distribution g(W) of the finish delivery-side width W output from the width prediction model M satisfies Expression (1) above with the aimed width W_t constant. FIG. 14 is a diagram illustrating a relationship between a deviation of the finish delivery-side width W from the aimed width W_t and a cut-off amount of the steel sheet. As can be seen from FIG. 14, even in a case where the finish delivery-side width W is too large or too small with respect to the aimed width W_t, the cut-off amount of the steel sheet is increased, and the product yield of the hot-rolled steel sheet is decreased. Specifically, in a case where the finish delivery-side width W is too large with respect to the aimed width W_t, it is necessary to perform the edge trimming in the subsequent processing in order for the hot-rolled steel sheet to satisfy the specification of the width. On the other hand, when the finish delivery-side width W is too small with respect to the aimed width W_t, a steel sheet product cannot be obtained, and a part thereof needs to be scrapped. However, the cut-off amount of the steel sheet is suppressed in a case where the finish delivery-side width W is too large than in a case where the finish delivery-side width W is too small with respect to the aimed width W_t. Therefore, Expression (1) above sets the operational parameters of the finish rolling mill 6 such that the probability that the finish delivery-side width W becomes too small is decreased even when the variation in the finish delivery-side width W with respect to the aimed width W_t occurs. That is, a lower limit value with respect to the aimed width W_t of Expression (1) is for decreasing the probability that the finish delivery-side width W becomes too small, and an upper limit value with respect to the aimed width W_t is for preventing the finish delivery-side width W from becoming too large with respect to the aimed width W_t.

In the width control method of the finished rolled material according to the present embodiment, the statistical information of the finish delivery-side width is output in response to not only classifications such as the steel type and size of the slab, and the product dimensions of the hot-rolled steel sheet, but also different operational conditions for each hot-rolled steel sheet, so that it is possible to predict the variation of the finish delivery-side width for each hot-rolled steel sheet. As a result, it is not necessary to set the extra width in advance according to the steel type and size classification of the steel sheet as in the related art, and it is possible to improve the product yield of the hot-rolled steel sheet by providing an appropriate extra width for each hot-rolled steel sheet manufactured in the hot rolling line. Furthermore, in the width control method of the finished rolled material of the present embodiment, the prediction step of predicting the statistical information of the finish delivery-side width may be executed as needed during a period from when the leading end portion of the rough rolled material is loaded into the finish rolling mill 6 until the trailing end portion passes through the finish rolling mill 6. Accordingly, so-called dynamic finish width control can be realized. Specifically, it is possible to acquire the actual value of the operational parameters of the finish rolling mill 6 at the present time during the finish rolling, and it is possible to predict the finish delivery-side width when the steel sheet loaded into the rolling stand F1 of the finish rolling mill 6 is unloaded from the rolling stand F7. Then, the statistical information of the finish delivery-side width is predicted as needed, and one or more operational parameters selected from the operational parameters of the finish rolling mill 6 are set as needed on the basis of the predicted statistical information such that the probability that the finish delivery-side width W falls below the aimed width W_t becomes small. As a result, even in a case where the width defect occurs in a part of the leading end portion of the hot-rolled steel sheet, it is possible to prevent the width defect in other regions, and to suppress a decrease in product yield. In this case, as the width data of the rough rolled material, it is preferable to use an actual measurement value of the width of the rough rolled material measured for each position in the longitudinal direction of the rough rolled material. This is because the width prediction accuracy for each position in the longitudinal direction of the hot-rolled steel sheet is improved, and the control accuracy of the width of the hot-rolled steel sheet is also improved.

EXAMPLES

First Example

In the present example, the width prediction method and the width control method of the steel sheet of the present invention were applied to the hot rolling line 1 which included the width reduction pressing device 4 positioned on the downstream side of the heating furnace 2, the rough rolling mill 5 including four reversible rolling mills and one non-reversible rolling mill, and the finish rolling mill 6 including seven rolling stands. In the present example, by the hot rolling line 1, a slab having a slab thickness of 250 to 270 mm and a slab width of 600 to 1600 mm was heated by the heating furnace 2 to manufacture a hot-rolled steel sheet having a sheet thickness of 30 to 35 mm on the delivery side of the rough rolling mill 5 and a sheet thickness of 2 to 3 mm on the delivery side of the finish rolling mill 6. In addition, the hot rolling line 1 included the rough delivery-side width meter 11, the finish delivery-side width meter 12, and the coiler entry width meter 13. In addition, the control computer 91 and the host computer 92 of the hot rolling line 1 collected the set value and the actual measurement value of the rough delivery-side width and the set value and the actual value of the operational parameter of the finish rolling mill 6, and the data acquisition unit 103 acquired these pieces of performance data. The data acquisition unit 103 acquired the actual measurement value of the width of the rough rolled material, the set values of the entry-side sheet thickness, the reduction amount, and the work roll peripheral speed in all the rolling stands, the work roll diameter, and the actual values of the temperatures of the leading end portion and the trailing end portion of the steel sheet measured on the entry side of the finish rolling mill 6 as the operational performance data of the finish rolling mill 6. On the other hand, the data acquisition unit 103 calculated the mean width of the steady portion of the steel sheet from the actual value of the finish delivery-side width meter 12, and used the mean width as the performance data of the finish delivery-side width. The performance data of the finish delivery-side width was associated with the above-described operational performance data by the data acquisition unit 103, and thereby one data set was generated for one finished rolled material, and was accumulated in the database unit 101. Then, when 30,000 data sets were accumulated in the database unit 101, these data sets were divided into 20,000 pieces of learning data and 10,000 pieces of test data, and the width prediction model M was generated by the machine learning unit 102 using the learning data. In the present example, a radial basis function (RBF) kernel was used as the kernel function for Gaussian process regression. In addition, noise having a constant variance σ_e² regardless of the learning data was used as the Gaussian noise. The kernel function used in the present example is represented by the following Expression (19). Here, ∥x⁽ⁱ⁾−x^(j)∥ represents a Euclidean distance between input vectors.

k ⁡ ( x ( i ) , x ( j ) ) = exp ⁡ ( -  x ( i ) - x ( j )  2 / 2 ⁢ θ 2 ) ( 19 )

In the present example, the hyperparameter of the width prediction model M was specified by the Gaussian process regression method using the learning data. Then, the operational performance data of the test data was input to the prediction unit 112 of the width prediction unit 110, and the mean value W_m and the standard deviation W_σ of the finish delivery-side width as the outputs of the width prediction model M were obtained. Then, the root mean square error (RMSE) was calculated from the deviation between the performance data W_a of the finish delivery-side width W and the mean value W_m of the finish delivery-side width as the test data. Furthermore, the number of pieces of test data in which the performance data W_a of the finish delivery-side width W falls within a range of W_m±W_σ and a range of W_m±1.96W_σ, was obtained, and the ratio of the number of pieces of test data falling within these ranges to all the pieces of test data was calculated. As a result, the RMSE calculated from the deviation between the performance data W_a of the finish delivery-side width W and the mean value W_m of the finish delivery-side width was as good as 0.1 mm. Furthermore, the probability that the finish delivery-side width W fell within the range of W_m±W_σ was 67.3%, and the probability that the finish delivery-side width W fell within the range of W_m±1.96W_σ was 95.3%. This means that in a case where it is assumed that the variation in the finish delivery-side width W follows the normal distribution, the probabilities are 68.3% and 95.0%, respectively, and thus it has been confirmed that the variation in the finish delivery-side width W can be accurately predicted by the width prediction model M of the present example. On the other hand, the width prediction model M generated as described above was stored in the prediction unit 112 of the width prediction unit 110, and width control was performed on a steel sheet having a slab width of 1000 to 1200 mm. In this case, the rough rolling was ended for each rough rolled material, the statistical information of the finish delivery-side width was calculated using the width prediction model M at the timing when the actual measurement value of the rough delivery-side width was acquired by the rough delivery-side width meter 11, and the operational parameters of the finish rolling mill 6 were reset such that the aimed width W_t of the finish delivery-side width W set for each steel sheet satisfied the relationship illustrated in Expression (1). As the operational parameter of the finish rolling mill 6 to be reset, the inter-rolling stand tension in the finish rolling mill 6 was selected. The steel sheet subjected to the finish rolling as described above was cooled in a run-out table to manufacture a hot-rolled steel sheet. The manufactured hot-rolled steel sheet was 400 coils. As a result, the ratio of the coil having the width falling below the coiler entry aimed width was reduced by 35% according to the present example as compared with the example in the related art in which the extra width is set in advance. In addition, the edge trimming allowance, which had been cut off due to the width exceeding the coiler entry aimed width, was reduced by 0.8 mm on average according to the present example. From the above, it was confirmed that the statistical information of the width of the finished rolled material can be predicted and applied to the width control of the finished rolled material according to the present example, thereby reducing the width defect of the hot-rolled steel sheet and improving the product yield.

Second Example

As an example of the present invention, another example of the width prediction method of the finished rolled material will be described. In the first example described above, when the performance data was accumulated in the database unit 101, the data acquisition unit 103 acquired the performance data of the thickness, the slab width, and the slab length of the slab, which were information regarding the slab dimension, as the attribute information of the slab. In addition, the data acquisition unit 103 acquired performance data of each content of C, Si, Mn, P, S, Nb, Ti, Cu, Ni, Mo, and B of the slab, which was the information regarding the composition of the slab, as the attribute information of the slab. Then, the performance data of the attribute information of the slab was accumulated in the database unit 101 as the data set associated with the performance data acquired in the data acquisition unit 103 in the first example.

In the present example, when 30,000 data sets were accumulated in the database unit 101, these data sets were divided into 20,000 pieces of learning data and 10,000 pieces of test data, and the width prediction model M was generated by the machine learning unit 102 using the learning data. In machine learning, the radial basis function (RBF) kernel was used as the kernel function for Gaussian process regression.

The width prediction model M generated in the present example is a width prediction model trained by the Gaussian process regression method using the actual measurement value of the width of the rough rolled material, the operational parameter of the finish rolling mill, and the parameter selected from the attribute information of the slab as the input data and using the statistical information of the width of the finished rolled material as the output data from the data set accumulated in the database unit 101. The operational parameters of the finish rolling mill used for the input data are the entry-side sheet thickness, the reduction amount, the work roll peripheral speed, and the work roll diameter in all the rolling stands of the finish rolling mill 6, and the temperatures of the leading end portion and the trailing end portion of the steel sheet on the entry side of the finish rolling mill, similarly to the first example. In addition, the parameters of the attribute information of the slab used for the input data are the thickness, the slab width, and the slab length of the slab, which are information regarding the slab dimension, and each content of C, Si, Mn, P, S, Nb, Ti, Cu, Ni, Mo, and B of the slab, which are information regarding the composition of the slab.

In the present example, the hyperparameter of the width prediction model M was specified by the Gaussian process regression method using the learning data. Then, the operational performance data of the test data was input to the prediction unit 112 of the width prediction unit 110, and the mean value W_m and the standard deviation W_σ of the finish delivery-side width W as the outputs of the width prediction model were obtained. In addition, the root mean square error (RMSE) was calculated from the deviation between the performance data W_a and the mean value W_m of the finish delivery-side width W as the test data. Furthermore, the number of pieces of test data in which the performance data W_a of the finish delivery-side width W falls within a range of W_m±W_σ was obtained, and the ratio of the number of pieces of test data falling within these ranges to all the pieces of test data was calculated.

As a result, according to the generated width prediction model M, the RMSE calculated from the deviation between the performance data W_a and the mean value W_m of the finish delivery-side width W was 0.0 mm. In addition, the probability that the finish delivery-side width W fell within the range of W_m±W_σ was 65.3%, which was a value close to the probability of 68.3% in a case where the variation in the finish delivery-side width W was assumed to follow the normal distribution. From the above, according to the present invention, it has been confirmed that the mean value W_m and the standard deviation W_σ of the finish delivery-side width, which are statistical information of the finish delivery-side width, can be accurately predicted.

Although the embodiments to which the invention made by the present inventors is applied have been described above, the present invention is not limited by the description and drawings constituting a part of the disclosure of the present invention according to the present embodiments. That is, other embodiments, examples, operation techniques, and the like made by those skilled in the art based on the present embodiment are all included in the scope of the present invention.

INDUSTRIAL APPLICABILITY

According to the present invention, it is possible to provide a width prediction method of a finished rolled material capable of predicting statistical information including variation in the width of the finished rolled material. In addition, according to the present invention, it is possible to provide a width control method of a finished rolled material capable of accurately controlling the width in the longitudinal direction of the finished rolled material in consideration of the variation in the width of the finished rolled material. In addition, according to the present invention, it is possible to provide a manufacturing method of a hot-rolled steel sheet capable of improving the product yield of the hot-rolled steel sheet. In addition, according to the present invention, it is possible to provide a generation method of a width prediction model of a finished rolled material capable of generating the width prediction model for predicting statistical information including the variation in the width of the finished rolled material.

REFERENCE SIGNS LIST

• • 1 HOT ROLLING LINE
  • 2 HEATING FURNACE
  • 3 DESCALING DEVICE
  • 4 WIDTH REDUCTION PRESSING DEVICE
  • 5 ROUGH ROLLING MILL
  • 6 FINISH ROLLING MILL
  • 7 COOLING DEVICE
  • 8 COILER (WINDING MACHINE)
  • 11 ROUGH DELIVERY-SIDE WIDTH METER
  • 12 FINISH DELIVERY-SIDE WIDTH METER
  • 13 COILER ENTRY WIDTH METER (COILER ENTRY-SIDE WIDTH METER)
  • 14 FINISH ENTRY-SIDE WIDTH METER
  • 15 PASS LINE
  • 16a, 16b, 16c, 16d CAMERA
  • 61 CROP SHEAR
  • 62a, 62b WORK ROLL
  • 63a, 63b BACK-UP ROLL
  • 64a, 64b BEARING PORTION (BACK-UP ROLL CHOCK)
  • 65 HOUSING
  • 66 LOAD CELL
  • 67 REDUCTION CYLINDER
  • 68a, 68b BEARING HOUSING (WORK ROLL CHOCK)
  • 69 LOOPER
  • 69a LOOPER ROLL
  • 90 CONTROL CONTROLLER
  • 91 CONTROL COMPUTER
  • 92 HOST COMPUTER
  • 100 WIDTH PREDICTION MODEL GENERATION UNIT
  • 101 DATABASE UNIT
  • 102 MACHINE LEARNING UNIT
  • 103 DATA ACQUISITION UNIT
  • 110 WIDTH PREDICTION UNIT
  • 111 INPUT DATA ACQUISITION UNIT
  • M WIDTH PREDICTION MODEL
  • SA ROUGH ROLLED MATERIAL
  • SB STEEL SHEET