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

FIELD

[0001]The present invention relates to a width prediction method of a rough rolled material, a width control method of the rough rolled material, a manufacturing method of a hot-rolled steel sheet, and a generation method of a width prediction model of the rough rolled material in a hot rolling line.

BACKGROUND

[0002]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 a 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 having five to seven 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 the manufacturing process 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 in a stage before the rough rolling is completed and the steel sheet 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.

[0003]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 predicting a width change amount before and after rolling of a slab using a prediction model configured on the basis of measurement values of a width and a temperature of the slab rolled by the rough rolling mill, and setting an opening degree of an edger on the basis of the predicted width change amount. In addition, Patent Literature 1 discloses that the setting accuracy of the width reduction is improved by combining opening degree setting by an electric motor and opening degree adjustment by a hydraulic pressure for the opening degree setting of the edger, and parameters of the prediction model are subjected to online adaptive correction on the basis of an actual value of the width of the slab.

[0004]In addition, Patent Literature 2 discloses a method of estimating a width of a finished rolled material using a width prediction model indicating a relationship between performance data representing a width of a slab and a rolling process and the width of the finished rolled material for the purpose of controlling the width of the slab to be subjected the rough rolling, by the edger and controlling the width of the finished rolled material to a target value. In addition, Patent Literature 2 discloses a method of, for a rolled material that has been rolled most recently, accumulating the deviation between an estimated value and an actual measurement value of a width of the rolled material after finish rolling, and correcting a target value of the width after finish rolling of the slab to be rolled next. According to Patent Literature 2, it is stated that the width of the rolled material can be accurately controlled according to the variation in the width of the slab after continuous casting.

[0005]In addition, Patent Literature 3 discloses a method in which, for a rough rolling mill of a hot rolling line, learning means that learns information of a rolled material at the entry side of the edger, information of each roll diameter of the edger and a horizontal rolling mill, and a relationship between each actual value of the width after edger rolling and the thickness after horizontal rolling and an actual value of the width after horizontal rolling; and prediction means that calculates a prediction value of the width of the rolled material after horizontal rolling according to knowledge obtained by the learning means are provided, and the method sets an opening degree of the edger such that a difference between the prediction value and a target value of the width after horizontal rolling predicted by the prediction means. In addition, Patent Literature 3 discloses that the learning means can be configured by a neural network.

CITATION LIST

Patent Literature

Non Patent Literature

SUMMARY

Technical Problem

[0010]However, the method disclosed in Patent Literature 1 uses, as a prediction model, a physical model that predicts a width widening behavior of a slab caused by an edger and a horizontal rolling mill. For this reason, a representative value of the width of the slab is calculated as the prediction value of the width of the slab, and it is not possible to predict the variation in the width of the slab. In addition, Patent Literature 1 discloses that the width of the slab varies due to the error between the actual value and the set opening degree of the edger, but does not consider the variation in the width of the slab due to factors other than the estimation accuracy of the set opening degree of the edger. Therefore, it is inevitable that the width of the rough rolled material becomes too small or too large due to the variation in temperature or the like of the rough rolled material.

[0011]On the other hand, Patent Literature 2 discloses that a width change of a slab in a rough rolling mill is estimated using a physical model representing a width contraction amount by an edger and a width widening amount by a horizontal rolling mill. However, the physical model calculates the representative value of the width of the slab, and does not predict the variation in the width of the slab. In addition, Patent Literature 2 discloses a method of correcting a target value of the width after rolling of the slab to be rolled next on the basis of the deviation between the estimated value and the actual measurement value of the width of the rolled material after finish rolling. However, the variation in the width of the rough rolled material is caused not only by the variation in the width of the slab after continuous casting, but also by other factors. For this reason, the variation in the width of the rough rolled material cannot be eliminated, and it is inevitable that the width of the rough rolled material becomes too small or too large.

[0012]In addition, Patent Literature 3 discloses that a width of a rough rolled material is predicted by learning means such as a neural network on the basis of operational performance data of an edger and a horizontal rolling mill. However, the prediction means of the width of the rough rolled material calculates the representative value of the width of the rough rolled material, and does not predict the variation in the width of the rough rolled material. Therefore, it is inevitable that the width of the rough rolled material becomes too small or too large due to the variation in temperature or the like of the rough rolled material.

[0013]As described above, in the rough width control in the related art, a method of improving the width accuracy of the rough rolled material by focusing on a specific event that causes variation in the width of the rough rolled material and suppressing the variation has been adopted. However, since the variation in the width of the rough rolled material also occurs due to, for example, the variation in the temperature and deformation resistance of the slab, it is difficult to completely eliminate the variation in the width of the rough rolled material. For this reason, the width of the rough rolled material may become too small or too large, and it is inevitable that poor width accuracy of the rough rolled material and a decrease in the product yield occur.

[0014]The present invention has been made to solve the above problems, and an object thereof is to provide a width prediction method of a rough rolled material capable of predicting statistical information including variation in a width of the rough rolled material. In addition, another object of the present invention is to provide a width control method of the rough rolled material capable of accurately controlling the width in a longitudinal direction of the rough rolled material in consideration of the variation in the width of the rough 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 a 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 the rough rolled material capable of generating the width prediction model that predicts the statistical information including the variation in the width of the rough rolled material.

Solution to Problem

[0015]To solve the problem and achieve the object, a width prediction method of a rough rolled material according to the present invention is the width prediction method predicting a width of the rough rolled material in a hot rolling line including a heating furnace configured to heat a slab, a rough rolling mill configured to manufacture the rough rolled material by performing rough rolling on the heated slab, and a finish rolling mill configured to manufacture a 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 a width of the rough rolled material by using a width prediction model trained by a Gaussian process regression method, the width prediction method for which an input data is data including one or more operational parameters selected from operational parameters of the rough rolling mill, and an output data is the statistical information of the width of the rough rolled material.

[0016]Moreover, the hot rolling line may include a width reduction pressing device that is disposed on an upstream side of the rough rolling mill and intermittently reduces a width of the slab heated by the heating furnace, and the width prediction model may include, as the input data, one or more operational parameters selected from operational parameters of the width reduction pressing device.

[0017]Moreover, the width prediction model may include, as the input data, one or more operational parameters selected from operational parameters of the heating furnace.

[0018]Moreover, the width prediction model may include, as the input data, one or more parameters selected from attribute information of the slab.

[0019]Moreover, a width control method of a rough rolled material according to the present invention is the width control method including a resetting step of predicting statistical information of a width of the rough rolled material using the width prediction method of the rough rolled material according to the present invention, and resetting one or more operational parameters selected from operational parameters of the rough rolling mill such that a probability that the width of the rough rolled material falls below a target width of the rough rolled material becomes small, on the basis of the predicted statistical information.

[0020]Moreover, the statistical information of the width of the rough rolled material may include a mean value W_m and a standard deviation W_σ of the width of the rough rolled material, and the resetting step may include a step of setting one or more operational parameters selected from operational parameters of the rough rolling mill such that the target width W_t of the rough rolled material satisfies a relationship illustrated in following Expression (1).

$\begin{array}{cc}{W}_m-2.5W_{\sigma }\leqq W_t\leqq W_m-1.5W_{\sigma }& \left(1\right)\end{array}$

[0021]Moreover, a manufacturing method of a hot-rolled steel sheet according to the present invention is the manufacturing method including a step of manufacturing a hot-rolled steel sheet by using the width control method of the rough rolled material according to the present invention.

[0022]Moreover, a generation method of a width prediction model of a rough rolled material according to the present invention is the generation method generating a width prediction model of predicting a width of the rough rolled material in a hot rolling line including a heating furnace configured to heat a slab, a rough rolling mill configured to manufacture the rough rolled material by performing rough rolling on the heated slab, and a finish rolling mill configured to manufacture a 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 one or more pieces of operational performance data selected from operational performance data of the rough rolling mill and performance data of the width of the rough rolled material; and a step of generating the width prediction model using a Gaussian process regression method in which one or more pieces of operational performance data selected from the operational performance data of the rough rolling mill is included as input performance data and statistical information of the width of the rough rolled material is output data, using the plurality of pieces of learning data acquired in the learning data acquisition step.

Advantageous Effects of Invention

[0023]With the width prediction method of the rough rolled material according to the present invention, it is possible to predict the statistical information including the variation in the width of the rough rolled material. In addition, with the width control method of the rough rolled material according to the present invention, it is possible to accurately control the width in the longitudinal direction of the rough rolled material in consideration of the variation in the width of the rough 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 rough rolled material according to the present invention, it is possible to generate the width prediction model that predicts the statistical information including the variation in the width of the rough rolled material.

BRIEF DESCRIPTION OF DRAWINGS

[0024]FIG. 1 is a schematic diagram illustrating a configuration example of a hot rolling line to which the present invention is applied.

[0025]FIG. 2 is a schematic diagram illustrating a configuration example of a heating furnace illustrated in FIG. 1.

[0026]FIG. 3 is a schematic diagram of the inside of the heating furnace illustrated in FIG. 1 as viewed from above.

[0027]FIG. 4 is a schematic diagram illustrating a configuration example of a width reduction pressing device illustrated in FIG. 1.

[0028]FIG. 5 is a diagram illustrating a configuration of a rolling stand constituting a rough rolling mill illustrated in FIG. 1.

[0029]FIG. 6 is a schematic diagram for describing an optical width measurement method.

[0030]FIG. 7 is a flowchart illustrating a flow of a model generation step according to an embodiment of the present invention.

[0031]FIG. 8 is a flowchart illustrating a flow of a prediction step according to an embodiment of the present invention.

[0032]FIG. 9 is a block diagram illustrating a configuration of a width prediction model generation unit according to an embodiment of the present invention.

[0033]FIG. 10 is a diagram for describing a setting method of a control target width in a width control method in the related art.

[0034]FIG. 11 is a block diagram illustrating a configuration of a width prediction unit according to an embodiment of the present invention.

[0035]FIG. 12 is a diagram illustrating a relationship between a probability density distribution of a rough delivery-side width predicted by a width prediction model and an aimed width.

[0036]FIG. 13 is a diagram for describing a setting method of a control target value in rough width control according to the present embodiment.

[0037]FIG. 14 is a diagram illustrating a relationship between a probability density distribution of a rough delivery-side width predicted by a width prediction model and an aimed width.

[0038]FIG. 15 is a diagram illustrating a relationship between a deviation of a rough delivery-side width from an aimed width and a cut-off amount of a steel sheet.

DESCRIPTION OF EMBODIMENTS

[0039]Hereinafter, a width prediction method of a rough rolled material, a width control method of a rough rolled material, a manufacturing method of a hot-rolled steel sheet, and a generation method of a width prediction model of a rough rolled material according to an embodiment of the present invention will be described in detail with reference to the drawings.

[Hot Rolling Line]

[0040]First, a configuration of a hot rolling line to which the present invention is applied will be described with reference to FIGS. 1 to 6.

[0041]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. Then, 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 five to seven 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 steel sheet before winding is installed on the delivery side of the cooling device 7. Hereinafter, 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.

[0042]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 the 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 target width of the finished rolled material (finish aimed width) 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 a rough aimed width (hereinafter, simply referred to as an aimed width in some cases) which is the target 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 of the width control (the rough control target width, the finish control target width, the coiler entry control target width) may be set by providing an extra width (margin) in advance with respect to the rough aimed width, the finished 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 mill 6 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.

[0043]A width prediction method of the rough rolled material according to an embodiment of the present invention is a method of predicting the rough delivery-side width. In addition, a width control method of the rough rolled material according to an embodiment of the present invention is a method of controlling the width of the rough rolled material such that the rough delivery-side width satisfies a predetermined relationship with a rough aimed width.

[Heating Furnace]

[0044]FIG. 2 is a schematic diagram illustrating a configuration example of the heating furnace 2 illustrated in FIG. 1. As illustrated in FIG. 2, in the present embodiment, a slab SA is loaded into the heating furnace 2 from the left side of FIG. 2. The temperature of the slab SA loaded into the heating furnace 2 may be cooled to about room temperature in a post-casting slab yard or may be a temperature of about 600° C. during cooling. In addition, the slab SA may be loaded at a temperature of about 600 to 800° C. without passing through the post-casting slab yard. The inside of the heating furnace 2 is divided into a plurality of zones, and a heating zone divided into two to eight zones and one to three soaking zones are generally provided on the upstream side. In the example illustrated in FIG. 2, five heating zones and one soaking zone are provided, and here, both are collectively referred to as a “heating furnace zone”. The individual heating furnace zones are set to different ambient temperatures such that the average temperature of the slab SA loaded into the heating furnace 2 is gradually increased to reach a predetermined target heating temperature (target value of the average temperature of the slab SA in a case of being extracted from the heating furnace 2). In addition, a thermometer 21 that measures an ambient temperature in the heating furnace zone is installed above any of the heating furnace zones.

[0045]FIG. 3 is a schematic diagram of the inside of the heating furnace 2 illustrated in FIG. 1 as viewed from above. As illustrated in FIG. 3, the slab SA loaded into the heating furnace 2 sequentially passes through each heating furnace zone by a conveyance facility called a walking beam 22 inside the heating furnace 2. In addition, a plurality of slabs SA are simultaneously loaded into the heating furnace 2, and are extracted from the extraction-side outlet of the heating furnace 2 in the order of being loaded into the heating furnace 2, and hot rolling is performed. The inside of the walking beam 22 is water-cooled, and a part where the temperature increase of the slab SA is locally hindered by a member called a skid, which comes into direct contact with the slab SA is generated. A part of the slab SA in contact with the skid is called a skid mark, and has a lower temperature than that of a part not in contact with the skid. The skid mark is one of the factors of variations in the rough delivery-side width.

[Width Reduction Pressing Device]

[0046]FIG. 4 is a schematic diagram illustrating a configuration example of the width reduction pressing device 4 illustrated in FIG. 1. The slab SA heated by 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. As illustrated in FIG. 4, the width reduction pressing device 4 includes a pair of width reduction dies 41. The width reduction dies 41 press down the slab SA from the width direction. The width reduction pressing device 4 drives the width reduction dies 41 by a driving device 42 while conveying the slab SA, and intermittently reduces the width of the slab SA from both sides of the slab SA in the width direction.

[0047]In the width reduction pressing device 4, the slab SA is conveyed using a pinch roller 43 or the like. The width reduction pressing device 4 can change a feed pitch of the slab SA between the width reduction passes by changing the driving amount of the pinch roller 43. The feed pitch means a conveyance distance of the slab SA for each pass in the width reduction in the width reduction pressing device 4. The driving amount of the pinch roller 43 is controlled by the control controller 90 that controls the width reduction pressing device 4. A parallel portion 41a parallel to a conveyance direction of the slab SA and an inclined portion 41b extending in the width direction toward a direction opposite to the conveyance direction of the slab SA are formed on a surface of the width reduction dies 41 in contact with the slab SA in order from the leading end side in the conveyance direction of the slab SA. In the width reduction dies 41, one or a plurality of parallel portions 41a may be provided between the inclined portions 41b in order to suppress occurrence of slip with respect to the slab SA. The shape of the width reduction dies 41 changes the deformation state of the slab SA and affects the rough delivery-side width.

[Rough Rolling Mill]

[0048]Returning to FIG. 1. The rough rolling mill 5 includes a reversible rolling mill 5a capable of reverse rolling and a non-reversible rolling mill 5b that allows rolling only in the conveyance direction to the downstream side Arrows (solid line) illustrated below the rough rolling mill 5 illustrated in FIG. 1 represent the reduction pass (a rolling pass for reducing the thickness). In the reversible rolling mill 5a, usually, about 5 to 11 reduction passes are performed in a reversible direction (from the upstream side to the downstream side or from the downstream side to the upstream side). In the final reduction pass, since rolling and conveyance to the next rolling mill are simultaneously executed, the number of rolling passes of the reversible rolling mill is always an odd number, and the steel sheet is conveyed to the rolling mill on the downstream side while being rolled. At this time, the time from when the trailing end portion of the steel sheet passes through the rolling mill in the present reduction pass to when the rolling direction is reversed and the steel sheet is meshed with the rolling mill in the next rolling pass is referred to as an inter-pass time of a reversible pass. In addition, in the final rolling pass of the reversible pass, the time from when the trailing end portion of the steel sheet passes through the reversible rolling mill 5a to when the steel sheet is meshed with the non-reversible rolling mill 5b is referred to as an inter-pass time of a continuous pass. Furthermore, the inter-pass time of the reversible pass and the inter-pass time of the continuous pass are collectively referred to as an inter-pass air cooling time. The inter-pass air cooling time represents time during which the slab is air-cooled during the conveyance, and affects the temperature change of the steel sheet.

[0049]FIG. 5 is a schematic diagram illustrating a configuration of a rolling stand constituting the rough rolling mill 5 illustrated in FIG. 1. As illustrated in FIG. 5, the rough rolling mill 5 includes a horizontal rolling mill 51 that reduces the thickness of a steel sheet SB, and an edger (vertical rolling mill) 52 that reduces the width of the steel sheet SB. The edger 52 is a rolling mill in which a pair of rolls is vertically arranged, and is installed adjacent to the horizontal rolling mill 51. The width reduction (width rolling) of the steel sheet SB using the edger 52 is usually performed before the horizontal rolling in each rolling pass of the rough rolling. Therefore, in a case where one edger 52 is disposed in the reversible rolling mill 5a, the width reduction by the edger 52 is performed only in the forward direction, that is, during the odd-numbered passes, and is not performed during the even-numbered passes, that is, in the passes in the reverse direction. However, in a case where the edgers 52 are arranged on both sides of the reversible rolling mill 5a, width reduction may be performed in any rolling pass. The roll opening degree (roll gap) of the horizontal rolling mill 51 and the opening degree of the edger 52 in each pass of the rough rolling are set by the control computer 91. In the rough rolling mill 5, a descaling header for injecting descaling water toward the steel sheet SB is installed, and descaling is performed on the entry side of the horizontal rolling mill 51. However, the descaling water is not necessarily injected in all the rolling passes of the rough rolling, and for example, a predetermined descaling pattern is set according to a material or the like of the steel sheet SB, such as injection only in the first pass or injection only in the odd-numbered passes. The steel sheet SB in a state where all the rolling passes set in advance are finished by the rough rolling mill 5 is referred to as a rough bar or a sheet bar, and is referred to as a rough rolled material in the present invention.

[Width Meter]

[0050]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, and the coiler entry width meter 13. 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 a camera. FIGS. 6(a) and 6(b) are schematic diagrams illustrating a configuration example of a rough delivery-side width meter using a camera. In the example illustrated in FIG. 6(a), a set of cameras 15a and 15b 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 15a and 15b, CMOS or CCD sensors are used. Then, an image processing unit provided in the rough delivery-side width meter specifies a position of the end portions of the steel sheet SB in the width direction from the images captured by the cameras 15a and 15b, and calculates a width W of the steel sheet S on the basis of the installation interval of the cameras 15a and 15b. Reference numeral 14 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 14. Therefore, the width meter often has a function of correcting a measurement error of the width in response to the floating of the steel sheet SB from the pass line. Specifically, as illustrated in FIG. 6(b), in a case where the steel sheet SB is conveyed at the height of a floating amount H from the pass line 14, the measurement error of the width is corrected as follows. That is, first, the set of cameras 15a and 15b arranged in the width direction of the steel sheet SB specifies both end portions of the steel sheet SB in the width direction, and thereby specifies a measurement value W1 of the width. Next, another set of cameras 15c and 15d arranged in the width direction of the steel sheet SB specifies both end portions of the steel sheet SB in the width direction, and thereby specifies a measurement value W2 of the width. Then, on the basis of a positional relationship between the two sets of cameras (in the example illustrated in FIG. 6(b), an interval D between the cameras 15a and 15b in the width direction and an interval L between the camera 15a (15b) and the camera 15c (15d) 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.

$\begin{array}{cc}W=\frac{\left(D+2L\right)W1-\mathrm{DW}1}{\left(W1-W2+2L\right)}& \left(2\right)\end{array}$

[0051]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 a conveyance speed of the steel sheet when 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 width of the steel sheet measured by the width meter may be represented by a deviation from the target width set in advance.

[Gaussian Process Regression]

[0052]The width prediction method of the rough rolled material according to an embodiment of the present invention predicts the rough delivery-side width in the hot rolling line 1. The width prediction method of the rough rolled material according to an embodiment of the present invention uses a width prediction model trained by a Gaussian process regression method in which one or more operational parameters selected from the operational parameters of the rough rolling mill 5 are included as input data and statistical information of the rough delivery-side width is output data. Hereinafter, the Gaussian process regression method applied to the width prediction method of the rough rolled material according to an embodiment of the present invention will be described.

[0053]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 value 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 rough 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.

[0054]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 value of zero and the variance of σ_e⁽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⁾.

$\begin{array}{cc}{y}^{\left(i\right)}=f\left(x^{\left(i\right)}\right)+{ϵ}^{\left(i\right)}& \left(3\right)\end{array}$

[0055]The Gaussian distribution refers to a distribution in which a 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.

$\begin{array}{cc}N\left(\mu ,{\sigma }^2\right)=\frac{1}{\sqrt{2{\mathrm{\pi \sigma }}^2}}·\exp \left(\frac{-\left(x-{\mu }^2\right)}{2{\sigma }^2}\right)& \left(4\right)\end{array}$

[0056]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 a parameter θ. Expression (5) represents a linear kernel, Expression (6) represents a second-order polynomial kernel, and Expression (7) represents a Gaussian kernel.

$\begin{array}{cc}k\left(x^{\left(i\right)},x^{\left(j\right)}\right)=\theta ·x^{\left(i\right)}·x^{\left(j\right)\tau }& \left(5\right)\end{array}$$\begin{array}{cc}k\left(x^{\left(i\right)},x^{\left(j\right)}\right)={\left(1+\theta ·x^{\left(i\right)}·x^{\left(j\right)\tau }\right)}^2& \left(6\right)\end{array}$$\begin{array}{cc}k\left(x^{\left(i\right)},x^{\left(j\right)}\right)=\exp \left(-{\left(x^{\left(i\right)},x^{\left(j\right)}\right)}^2/\theta \right)& \left(7\right)\end{array}$

[0057]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.

$\begin{array}{cc}\left[\begin{array}{c}{y}^{\left(1\right)}\\ ⋮\\ y^{\left(n\right)}\end{array}\right]=\left[\begin{array}{c}{f}^{\left(1\right)}\\ ⋮\\ f^{\left(n\right)}\end{array}\right]+\left[\begin{array}{c}{\sigma }_e^{{\left(1\right)}^2}\\ ⋮\\ {\sigma }_e^{{\left(n\right)}^2}\end{array}\right]=N\left(\left[\begin{array}{c}0\\ ⋮\\ 0\end{array}\right],\left[\begin{array}{ccc}k\left(x^{\left(1\right)},x^{\left(1\right)}\right)& \dots & k\left(x^{\left(1\right)},x^{\left(n\right)}\right)\\ ⋮& \ddots & ⋮\\ k\left(x^{\left(n\right)},x^{\left(1\right)}\right)& \dots & k\left(x^{\left(n\right)},x^{\left(n\right)}\right)\end{array}\right]\right)+\left[\begin{array}{c}{\sigma }_e^{{\left(1\right)}^2}\\ ⋮\\ {\sigma }_e^{{\left(n\right)}^2}\end{array}\right]& \left(8\right)\end{array}$

[0058]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.

$\begin{array}{cc}{K}_n=\left[\begin{array}{ccc}k\left(x^{\left(1\right)},x^{\left(1\right)}\right)& \dots & k\left(x^{\left(1\right)},x^{\left(n\right)}\right)\\ ⋮& \ddots & ⋮\\ k\left(x^{\left(n\right)},x^{\left(1\right)}\right)& \dots & k\left(x^{\left(n\right)},x^{\left(n\right)}\right)\end{array}\right]& \left(9\right)\end{array}$$\begin{array}{cc}{\sum }_n=\left[\begin{array}{ccc}k\left(x^{\left(1\right)},x^{\left(1\right)}\right)+{\sigma }_e^2& \dots & k\left(x^{\left(1\right)},x^{\left(n\right)}\right)\\ ⋮& \ddots & ⋮\\ k\left(x^{\left(n\right)},x^{\left(1\right)}\right)& \dots & k\left(x^{\left(n\right)},x^{\left(n\right)}\right)+{\sigma }_e^2\end{array}\right]& \left(10\right)\end{array}$$\begin{array}{cc}{y}^{\left(i\right)}=N\left(0,K_n+{\sigma }_e^{2}I\right)& \left(11\right)\end{array}$$\begin{array}{cc}{y}^{\left(i\right)}=N\left(0,{\sum }_n\right)& \left(12\right)\end{array}$

[0059]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 such that the relationship illustrated 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.

[0060]Next, a method will be described which estimates the statistical information y* of the rough 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).

$\begin{array}{cc}\left[\begin{array}{c}{y}^{\left(1\right)}\\ ⋮\\ y^{\left(n\right)}\\ y^{*}\end{array}\right]=N\left(\left[\begin{array}{c}0\\ 0\\ ⋮\\ 0\end{array}\right],\left[\begin{array}{cccc}k\left(x^{\left(1\right)},x^{\left(1\right)}\right)+{\sigma }_e^2& \dots & k\left(x^{\left(1\right)},x^{\left(n\right)}\right)& k\left(x^{\left(1\right)},x^{*}\right)\\ ⋮& \ddots & ⋮& ⋮\\ k\left(x^{\left(n\right)},x^{\left(1\right)}\right)& \dots & k\left(x^{\left(n\right)},x^{\left(n\right)}\right)+{\sigma }_e^2& k\left(x^{\left(n\right)},x^{*}\right)\\ k\left(x^{*},x^{\left(1\right)}\right)& \dots & k\left(x^{*},x^{\left(n\right)}\right)& k\left(x^{*},x^{*}\right)+{\sigma }_e^2\end{array}\right]\right)& \left(13\right)\end{array}$$\begin{array}{cc}{k}^{*}=\left[\begin{array}{c}k\left(x^{\left(1\right)},x^{*}\right)\\ ⋮\\ k\left(x^{\left(n\right)},x^{*}\right)\end{array}\right]& \left(14\right)\end{array}$

[0061]As a result, Expression (13) can be represented as the following Expression (15). Then, the statistical information y* of the rough delivery-side width 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.

$\begin{array}{cc}\left[\begin{array}{c}{y}^{\left(1\right)}\\ ⋮\\ y^{\left(n\right)}\\ y^{*}\end{array}\right]=N\left(\left[\begin{array}{c}0\\ 0\\ ⋮\\ 0\end{array}\right],\left[\begin{array}{cc}{\sum }_n& k^{*}\\ k^{*T}& k\left(x^{*},x^{*}\right)+{\sigma }_e^2\end{array}\right]\right)& \left(15\right)\end{array}$$\begin{array}{cc}{W}_m\left(x^{*}\right)=k^{*}·{\sum }_n^{-1}·\left[\begin{array}{c}{y}^{\left(1\right)}\\ ⋮\\ y^{\left(n\right)}\end{array}\right]& \left(16\right)\end{array}$$\begin{array}{cc}{W}_{\sigma }\left(x^{*}\right)=\sqrt{k\left(x^{*},x^{*}\right)+{\sigma }_e^2-k^{*}·{\sum }_n^{-1}·k^T}& \left(17\right)\end{array}$

[0062]In the present embodiment, a step of specifying the hyperparameter 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. 7, 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 σ_e² 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 y* of the rough delivery-side width 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. 8, 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 of the statistical information y* of the rough delivery-side width 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).

[Generation Method of Width Prediction Model]

[0063]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 rough rolled material according to an embodiment of the present invention.

[0064]FIG. 9 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. 9, 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, one or more pieces of operational performance data selected from the operational performance data of the rough rolling mill 5, and performance data of the rough 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 the width reduction pressing device 4, one or more pieces of operational performance data selected from the operational performance data of the heating furnace 2, and one or more pieces of performance data selected from the performance data of attribute information of the slab SA as necessary. Specific performance data accumulated in the database unit 101 will be described later.

[0065]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 the 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 steel sheet is used as the performance data of the rough delivery-side width, the operational performance data of the rough rolling mill 5 may be represented using the representative value as the performance data. In this case, for the operational performance data of the width reduction pressing device 4, the operational performance data of the heating furnace 2, and the performance data of the attribute information of the slab SA, a representative value for one steel sheet may be used as the performance data.

[0066]On the other hand, a plurality of data sets may be generated for one steel sheet manufactured from one slab in the data acquisition unit 103, and 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 rough rolled material is acquired as the performance data of the rough delivery-side width, for the operational performance data of the rough rolling mill 5, the operational performance data acquired at each of the leading end portion, the steady portion, and the trailing end portion of the rough rolled material may be associated with the performance data of the rough 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 rough delivery-side width at the leading end portion, the steady portion, and the trailing end portion of the rough rolled material.

[0067]Furthermore, the data acquisition unit 103 may acquire the performance data of the rough delivery-side width for each position divided in the longitudinal direction with respect to one rough rolled material, and the operational performance data acquired for each position in the longitudinal direction of the rough rolled material may be accumulated in the database unit 101 in association with the performance data of the rough delivery-side width measured at each position. That is, the number of divisions in the longitudinal direction of the rough rolled material is set to, for example, about 20 to 200, and the performance data of the rough 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 rough-rolled by the rough rolling mill 5 is changed for each rough rolling pass, in a case where the operational performance data at the position corresponding to the division in the longitudinal direction of the rough rolled material is acquired, the data acquisition unit 103 can configure the data set corresponding to each divided section. In a case where data sets corresponding to a plurality of positions divided in the longitudinal direction of the rough rolled material 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 rough rolled material.

[0068]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 as 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 are accumulated in the database unit 101. Screening may be performed on the data accumulated in the database unit 101 as necessary.

[0069]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 one or more pieces of operational performance data selected from the operational performance data of the rough rolling mill 5 and performance data of the rough 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 one or more pieces of operational performance data selected from the operational performance data of the rough rolling mill 5 are included as input performance data and the statistical information of the rough 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 one or more pieces of operational performance data selected from the operational performance data of the width reduction pressing device 4, one or more pieces of operational performance data selected from the operational performance data of the heating furnace 2, and one or more pieces of performance data of the attribute information of the slab SA as the input performance data by using the data set accumulated in the database unit 101.

[0070]The machine learning in this case refers to specifying the hyperparameter applied to the Gaussian process regression by the model generation step illustrated in FIG. 7. 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 rough delivery-side width with respect to the unknown input can be predicted. In addition, in the present embodiment, the statistical information of the rough 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 rough rolled material and the standard deviation or variance which is an index representing the variation thereof. As a result, the variation of the rough delivery-side width can be predicted together with the mean value of the finish delivery-side width.

[0071]On the other hand, in the related art, for example, as disclosed in Patent Literature 3, the mean value or the representative value of the width change amount of the rough rolled material is predicted on the basis of the database generated by using the performance data related to the width change amount of the rough rolled material. However, in the related art, it is not possible to obtain information regarding the variation in the width change amount of the rough rolled material. Therefore, it is necessary to set a target value of the width of the rough rolled material by adding a preset extra width (margin). Specifically, in the width control method in the related art, as illustrated in FIG. 10, an extra width (margin) W_r is set in advance with respect to the target width (aimed width) W_t of the rough delivery-side width, and the sum of the aimed width W_t and the extra width W_r is set as a control target value W_c of the rough delivery-side width. The reason for setting the extra width W_r is to prevent the rough delivery-side width from falling below the aimed width W_t since a certain variation occurs in the rough delivery-side width. When the rough delivery-side width falls below the aimed width W_t, the width of the steel sheet after finish 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 finish 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 rough 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 related art, the performance data of the rough delivery-side width 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.

[0072]On the other hand, according to the present embodiment, since the mean value and the statistical variation of the rough 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 of each rough rolled material instead of each classification of the thickness and the width of the hot-rolled steel sheet as 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 rough delivery-side width.

[Attribute Information of Slab]

[0073]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 slab in the width reduction pressing device 4 and the rough rolling mill 5 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 slab in the hot rolling line 1, and thus affects the variation in the rough delivery-side width. In addition, the information regarding the composition of the slab affects the deformation resistance of the slab and the composition and thickness of an oxide film generated on the surface of the slab. As a result, the frictional force at an interface between the rolling roll and the slab is affected, and the deformation state of the slab is changed, so that the variation in the rough delivery-side width is affected.

[Operational Parameter of Heating Furnace]

[0074]The operational parameter of the heating furnace that can be used for the input of the width prediction model M is a parameter representing the operational condition of the heating furnace 2 in a case of heating the slab in the heating furnace 2, and refers to information that affects the width change of the slab in the width reduction pressing device 4 and the rough rolling mill 5. As the operational parameter of the heating furnace 2, the temperature of the slab in a case of being loaded into the heating furnace 2, the in-furnace time of the slab in a specific heating furnace zone in the heating furnace 2, the ambient temperature of the final heating furnace zone of the heating furnace 2, and the temperature of the slab extracted from the heating furnace 2 can be used. These parameters affect the temperature drop during the rough rolling of the slab, so that these parameters affect the rough delivery-side width.

[0075]In addition, information such as the loading position of the slab in the heating furnace 2 and the positional relationship of the slab with another slab in the heating furnace 2 may be used. As illustrated in FIG. 3, as the loading position of the slab in the heating furnace 2, information on an in-furnace loading position P, which represents the distance between a walking beam 22 located at one end portion of the heating furnace 2 and the end portions of the slab SA in the longitudinal direction can be used. The position of the skid mark in the longitudinal direction of the slab SA is changed by the in-furnace loading position P, the width variation in the longitudinal direction of the slab SA is affected, and thereby the variation in the rough delivery-side width is affected. As the loading position of the slab SA, a distance D1 between the end portion of the slab SA in the longitudinal direction and a furnace wall of the heating furnace 2, and a parameter representing the interval between the walking beam 22 (fixed skid) and a moving skid 23 of the heating furnace 2 loaded with the slab SA may be used. In addition, as the information on the positional relationship of the slab with another slab in the heating furnace 2, a distance (loading interval) D2 between the slab and another adjacent slab in the heating furnace 2 can be used. In a case where the loading interval D2 is changed in the heating furnace 2, the temperature at the end surface of the slab SA is changed. The temperature distribution of the slab SA in the hot rolling line 1 is affected, and thus the variation in the rough delivery-side width is affected. As the information on the positional relationship between the slab and another slab in the heating furnace 2, the length and thickness of another slab, the difference in distance from the leading end portion of the slab as a prediction target and the leading end portion of another slab to the furnace wall of the heating furnace, and the like may be used.

[Operational Parameter of Width Reduction Pressing Device]

[0076]The operational parameter of the width reduction pressing device 4 that can be used for the input of the width prediction model M refers to an operational condition when the width reduction is performed on the heated slab. As the operational parameter of the width reduction pressing device 4, an operational parameter regarding the width reduction amount with respect to the slab can be used. The operational parameter regarding the width reduction amount with respect to the slab includes the width reduction amount at a representative position in the longitudinal direction of the slab and the feed pitch of the slab between the width reduction passes. The operational parameters regarding the width reduction amount with respect to the slab may include a width reduction start position which is the length by which the parallel portion 41a of the width reduction dies 41 comes into contact with the slab in the initial width reduction pass with respect to the leading end portion of the slab. The operational parameters regarding the width reduction amount of the slab affect a dog-bone shape (thickness distribution in the width direction) formed on the slab after width reduction, and thereby affects the variation in the rough delivery-side width. That is, even in a case where the width reduction amount of the slab is constant in the longitudinal direction of the slab, the dog-bone shape is different at the steady portion, the leading end portion, and the trailing end portion of the slab. As a result, the mean value of the rough delivery-side width is changed, and the variation in the rough delivery-side width is affected. In addition, even in a case where the feed pitch of the slab between the width reduction passes is constant, there is a difference in the dog-bone shape between the steady portion and the leading and trailing end portions of the slab. As a result, the variation in the rough delivery-side width is affected.

[0077]Furthermore, as the operational parameter of the width reduction pressing device 4, the operational parameter regarding a die shape applied to the width reduction pressing device 4 can be used. The operational parameter regarding the die shape is a fixed representative value with respect to the longitudinal direction of the slab. For example, the length of the parallel portion 41a or the angle of the inclined portion 41b of the width reduction dies 41 illustrated in FIG. 4 may be used. The deformation state of the slab varies depending on the shape of the width reduction dies 41, and the variation in the rough delivery-side width is affected. In addition, the width reduction dies 41 have been ground offline and installed in the width reduction pressing device 4, and cumulative values of the slab length and the total weight of the slab that has been subjected to the width reduction using the width reduction dies 41 may be used as the operational parameter of the width reduction pressing device 4. This is because as the cumulative values of the slab length and the total weight of the slab are increased, wear and damage of the width reduction dies 41 progress, and an error occurs between the set value and the actual value of the width reduction amount, thereby causing variation in the rough delivery-side width.

[Operational Parameter of Rough Rolling Mill]

[0078]The operational parameter of the rough rolling mill used for the input of the width prediction model M means a rolling operational condition that affects the width of the steel sheet in an arbitrary rolling pass of the rough rolling by the rough rolling mill 5. The operational parameter of the rough rolling mill 5 preferably includes rolling conditions by the horizontal rolling mill 51 and the edger 52 constituting the rough rolling mill 5. As the rolling condition of the horizontal rolling mill 51, a roll opening degree, a work roll diameter, an entry-side sheet thickness, a delivery-side sheet thickness, a reduction ratio, a rough target width, a rolling load, and a steel sheet temperature in an arbitrary rolling pass may be used. This is because these affect the width widening behavior of the steel sheet in horizontal rolling, thereby affecting the variation in the rough delivery-side width. As the rolling condition of the edger 52, an edger opening degree, an edger roll diameter, a sheet thickness, a width reduction ratio, and a width reduction load in an arbitrary rolling pass may be used. These rolling conditions affect the width widening behavior of the steel sheet in horizontal rolling, thereby affecting the variation in the rough delivery-side width. In addition, even in a case where the operational condition in the width rolling is constant, there is a difference in the dog-bone formation behavior between the steady portion and the leading and trailing end portions of the steel sheet, which affects the width distribution in the longitudinal direction of the steel sheet and thereby affects the variation in the rough delivery-side width.

[0079]In addition, the work roll used in the horizontal rolling mill 51 and the edger roll used in the edger 52 have been ground offline and installed in the rough rolling mill 5, and cumulative values of the length and the total weight of the steel sheet that has been subjected to the rough rolling using the installed work roll and edger roll may be used as the operational parameter of the rough rolling mill 5. This is because as the cumulative values of the length and the total weight of the steel sheet are increased, wear and damage of the work roll and the edger roll progress, and an error occurs between the set value and the actual value of the width reduction amount by the reduction ratio and the edger in the horizontal rolling, thereby causing variation in the width of the steel sheet. Since the rolling conditions as the operational parameters of the rough rolling mill 5 greatly affect the width of the steel sheet, it is preferable to use the operational parameters selected from the operational parameters of all the rolling passes of the rough rolling process for the input of the width prediction model M. Specifically, the operational parameter of the rough rolling mill 5 may include a set value or an actual value of the delivery-side sheet thickness from the first pass to the final pass of the rough rolling. It is a so-called pass schedule of rough rolling. In a case where the pass schedule is different, the thickness of the steel sheet in a case of being conveyed between the rough passes is changed, so that the temperature distribution at the time of air cooling is changed. As a result, the deformation behavior in the width direction of the steel sheet varies depending on the position in the longitudinal direction of the steel sheet, and the variation in the rough delivery-side width is affected. Furthermore, the operational parameter of the rough rolling mill 5 may include information regarding the air cooling time between the rolling passes of the rough rolling and the presence or absence of injection of descaling water in an arbitrary rolling pass. This is because the variation in the temperature of the steel sheet affects the variation in the rough delivery-side width.

[Width Prediction Method of Rough Rolled Material]

[0080]A width prediction method of the rough rolled material according to an embodiment of the present invention includes a prediction step of predicting statistical information of the rough delivery-side width using the width prediction model M generated as described above. A 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. 11.

[0081]The operation of a width prediction unit 110 illustrated in FIG. 11 is executed before the rough delivery-side width of the steel sheet manufactured in the hot rolling line 1 is measured by the rough delivery-side width meter 11. 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 as the slab to 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, in the stage when the slab is loaded into the heating furnace 2, manufacturing specifications of the hot-rolled steel sheet are set, 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 conditions corresponding to the manufacturing specifications of the hot-rolled steel sheet as inputs. In addition, the prediction step can also be performed, for example, in a stage when the steel sheet as the prediction target is extracted as the slab from the heating furnace 2. In this case, the performance data of the operational parameters of the heating furnace 2 can be acquired, and can be used for input of the width prediction model M. Furthermore, the prediction step can be executed, for example, in a stage after the steel sheet as the prediction target is subjected to the width reduction by the width reduction pressing device 4. For the slab after width reduction, the performance data of the operational parameters of the width reduction pressing device 4 is acquired by the control computer 91 or the host computer 92. This is because the acquired performance data is used for the input of the width prediction model M, and the input of the width prediction model M is specified because the set value of the operational parameter of the rough rolling mill 5 is set by the control computer 91.

[0082]The operation of the width prediction unit 110 can also be executed, for example, in the middle of the rolling pass of the steel sheet by the rough rolling mill 5. This is because the performance data of the operational parameters of the rough rolling mill 5 in the rolling pass before the rolling pass at the present time is acquired by the control computer 91 or the host computer 92, and the set value of the operational parameters of the rough rolling mill 5 in the rolling pass after the present time can be acquired by the control computer 91 or the host computer 92. In any case, the width prediction unit 110 can predict the statistical information of the rough delivery-side width by inputting the actual value of the operational parameter in the process or pass on the upstream side of the process at the present time and the set value of the operational parameter until the rough rolling is completed, to the width prediction model M.

[0083]As described above, an input data acquisition unit 111 of the width prediction unit 110 illustrated in FIG. 11 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 as described above. 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. Then, the prediction unit 112 calculates a kernel function for the input data (new input vector) by the prediction step illustrated in FIG. 8, and calculates statistical information of the rough delivery-side width which is output data. As described above, since the operation of the width prediction unit 110 can be executed at each stage when the steel sheet passes through each process up to the delivery side of the rough rolling mill 5 in the hot rolling line 1, the operation may be executed a plurality of times in the process of manufacturing one steel sheet. The statistical information of the rough delivery-side width output as described above may be displayed on a monitor or the like connected to the width prediction unit 110. At least one of the operational parameters of the rough rolling mill 5 and the finish rolling mill 6 is reset on the basis of the output display of the statistical information of the rough delivery-side width, and the occurrence of the width defect of the hot-rolled steel sheet can be suppressed.

[Width Control Method of Rough Rolled Material]

[0084]The width control method of the rough rolled material according to an embodiment of the present invention resets one or more operational parameters selected from the operational parameters of the rough rolling mill 5 on the basis of the statistical information of the rough delivery-side width predicted as described above such that the probability that the rough delivery-side width falls below the aimed width Wt becomes small. In the width prediction method of the rough rolled material, the statistical information of the rough delivery-side width, which is the output of the width prediction model M, is specified as, for example, the mean value W_m and the standard deviation W_σ of the rough delivery-side width. In this case, the rough delivery-side width W is predicted to follow a probability density distribution g(W) illustrated in the following Expression (18).

$\begin{array}{cc}g\left(W\right)=\frac{1}{\sqrt{2\pi W_{\sigma }^2}}\exp \left(-\frac{{\left(W-W_m\right)}^2}{2W_{\sigma }^2}\right)& \left(18\right)\end{array}$

[0085]FIG. 12 is an example schematically illustrating the probability density distribution g(W) of the rough delivery-side width W predicted by the width prediction model M together with the aimed width W_t. In the example illustrated in FIG. 12, it is predicted that the rough 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 rough 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 rough delivery-side width W. In this case, it is predicted that the rough 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 example, one or more operational parameters selected from the operational parameters of the rough rolling mill 5 are reset such that the probability that the prediction value W of the rough delivery-side width W falls below the aimed width W_t becomes small. Specifically, the operational parameters of the rough rolling mill 5 are corrected such that the probability density distribution g(W) indicated by the solid line in FIG. 12 becomes the probability density distribution indicated by the broken line. In this case, as the operational parameters of the rough rolling mill 5 to be reset, the operational parameters in the rolling pass in which rolling is not performed at the present time are selected. In addition, the operational parameters to be reset are preferably selected from the operational parameters used for the input of the width prediction model M. In the example illustrated in FIG. 12, statistical information of the rough delivery-side width W is output using again the reset operational parameters of the rough rolling mill 5 as the input of the width prediction model M, and it is checked whether or not the probability that the statistical information of the output rough delivery-side width W falls below the aimed width W_t becomes small. As a result, it is possible to determine whether or not the proper operational condition is reset.

[0086]In addition, as illustrated in FIG. 13, in a case where the probability that the rough 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 rough delivery-side width W predicted by the width prediction model M, the control target value W_c of the rough width control may be set such that the probability that the rough delivery-side width W falls below the aimed width W_t becomes small. As a result, the rough 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 rough 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 rough rolling mill 5 are preferably reset such that the aimed width W_t satisfies the following Expression (1).

$\begin{array}{cc}{W}_m-2.5W_{\sigma }\leqq W_t\leqq W_m-1.5W_{\sigma }& \left(1\right)\end{array}$

[0087]FIG. 14 is a schematic diagram illustrating a relationship between the probability density distribution g(W) of the rough delivery-side width 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-2.5 W_σ and W_m-1.5 W_σ specified by the standard deviation W_σ and the mean value W_m of the rough delivery-side width W output from the width prediction model M. In this case, one or more operational parameters selected from the operational parameters of the rough rolling mill 5 may be reset such that the probability density distribution g(W) of the rough delivery-side width W output from the width prediction model M satisfies Expression (1) above with the aimed width W_t constant. FIG. 15 is a diagram illustrating a relationship between a deviation of the rough 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. 15, even in a case where the rough 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 rough 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 process in order for the hot-rolled steel sheet to satisfy the specification of the width. On the other hand, in a case where the rough 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 rough delivery-side width W is too large than in a case where the rough 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 rough rolling mill 5 such that the probability that the rough delivery-side width W becomes too small is decreased even when the variation in the rough 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 rough delivery-side width W becomes too small, and an upper limit value with respect to the aimed width W_t is for preventing the rough delivery-side width W from becoming too large with respect to the aimed width W_t.

[0088]In the width control method of the rough rolled material according to the present embodiment, the statistical information of the rough 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 rough rolled material, so that it is possible to predict the variation in the rough delivery-side width for each rough rolled material. 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 rough rolled material manufactured in the hot rolling line.

EXAMPLES

First Example

[0089]In an example of the present invention, the width prediction and the width control of the rough rolled material were performed in the hot rolling line 1 including the width reduction pressing device 4 disposed on the downstream side of the heating furnace 2, the rough rolling mill 5 including four reversible rolling mills 5a and one non-reversible rolling mill 1b, 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 produce a hot-rolled steel sheet having a sheet thickness on the delivery side of the rough rolling mill 5 of 30 to 35 mm and a sheet thickness on the delivery side of the finish rolling mill 6 of 2 to 3 mm. In addition, the hot rolling line 1 includes the rough delivery-side width meter 11, the finish delivery-side width meter 12, and the coiler entry width meter 13.

[0090]The control computer 91 or the host computer 92 of the hot rolling line 1 collected actual values of the operational parameters of the rough rolled material manufactured in the hot rolling line 1, and acquired the performance data by the data acquisition unit 103. The data acquisition unit 103 acquired, as the operational performance data of the rough rolling mill 5, the edger opening degree, the diameter of the edger roll, and the total rolling length after grinding of the edger roll in all the rolling passes of the rough rolling. In addition, as the operational performance data of the rough rolling mill 5, the work roll diameter, the entry-side sheet thickness, the delivery-side sheet thickness, and the total rolling length after grinding of the work roll of the horizontal rolling mill in all the rolling passes of the rough rolling were acquired. Furthermore, the data acquisition unit 103 acquired the data of the thickness and the width of the slab as the performance data of the attribute information of the slab.

[0091]On the other hand, the data acquisition unit 103 calculated the mean width of the steady portion from the actual value of the rough delivery-side width measured by the rough delivery-side width meter 11, and used the mean width as the performance data of the rough delivery-side width. The performance data of the rough delivery-side width was associated with the above-described operational performance data by the data acquisition unit 103 to configure one data set for one rough rolled material, and was accumulated in the database unit 101. Then, in a stage 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 of the 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.

$\begin{array}{cc}k\left(x^{\left(i\right)},x^{\left(j\right)}\right)=\exp (-{x^{\left(i\right)}-x^{\left(j\right)}}^2/2{\theta }^2& \left(19\right)\end{array}$

[0092]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 rough delivery-side width W as the outputs of the width prediction model M 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 rough 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 rough 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.

[0093]As a result, the RMSE calculated from the deviation between the performance data W_a and the mean value W_m of the rough delivery-side width W was as good as 0.1 mm. Furthermore, the probability that the rough delivery-side width W fell within the range of W_m±W_σ was 67.3%, and the probability that the rough 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 rough 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 rough 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 the rough rolled material having a slab width of 1000 to 1200 mm. In this case, the statistical information of the rough delivery-side width W was calculated using the width prediction model M at the timing when the slab was extracted from the heating furnace 2 for each steel sheet, and the operational parameters of the rough rolling mill 5 were reset such that the aimed width W_t of the rough rolled material set for each steel sheet satisfied the relationship illustrated in Expression (1). As the operational parameter of the rough rolling mill 5 to be reset, the edger opening degree of the rough rolling mill 5 was selected. The rough rolled material subjected to the rough rolling as described above was subsequently subjected to the finish rolling to produce 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 of the hot-rolled steel sheet falling below the coiler entry aimed width was reduced by 35% 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, according to the present example, it was confirmed that by predicting the statistical information of the rough delivery-side width and applying the predicted statistical information of the rough delivery-side width to the width control of the rough rolled material, the width defect of the hot-rolled steel sheet was reduced, and the product yield was improved.

Second Example

[0094]As an example of the present invention, another example of the width prediction method of the rough 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 operational performance data of the width reduction pressing device 4 and the operational performance data of the heating furnace 2, and accumulated the acquired operational performance data in association with the operational performance data of the rough rolling mill 5 and the performance data of the attribute information of the slab. In the present example, by using the performance data accumulated in the database unit 101 as described above, the input data used for the width prediction model M was changed, and the width prediction accuracy of the rough rolled material was evaluated.

[0095]The operational performance data of the width reduction pressing device 4 accumulated in the database unit 101 is a width reduction amount SPW of the slab, a feed pitch SPP of the slab between the width reduction passes, and a width reduction start position SPS. As the width reduction amount SPW of the slab and the feed pitch SPP of the slab between the width reduction passes, the width reduction amount and the feed pitch in the steady portion of the slab were used. In addition, the operational performance data of the heating furnace 2 accumulated in the database unit 101 is an in-furnace time IFT from when the slab is loaded into the heating furnace 2 to when the slab is extracted from the heating furnace 2, a temperature (extraction temperature) ET of the slab extracted from the heating furnace 2, and a distance D1 between a furnace wall of the heating furnace 2 and the end portions of the slab in the longitudinal direction as the operational parameter regarding the loading position of the slab in the heating furnace 2.

[0096]Even in the present example, in a stage when 30,000 data sets were accumulated in the database unit 101, the 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 this case, the machine learning unit 102 executed the machine learning by changing the variables used for the input data of the width prediction model M, and generated the width prediction model M corresponding to each condition. In any condition, a radial basis function (RBF) kernel was used as the kernel function of the Gaussian process regression.

[0097]Table 1 shows input data used for each width prediction model. Each of the width prediction models No. 1 to 3 in Table 1 includes the operational parameters of the rough rolling mill 5 as the input data. As the operational parameters of the rough rolling mill 5, an edger opening degree EG of the steady portion and a diameter ED of the edger roll in all the rolling passes of the edger rough rolling were used. Furthermore, as the operational parameters of the rough rolling mill 5, an entry-side sheet thickness HI and a delivery-side sheet thickness HO of the steady portion, and a work roll diameter HWD of the horizontal rolling mill in all the rolling passes of the rough rolling were used. However, in the present example, the parameter of the attribute information of the slab was not used as the input data of the width prediction model M.

[0098]In the width prediction model No. 1 shown in Table 1, only the parameters of the rough rolling mill 5 described above were used as the input data. In the width prediction model No. 2, the operational parameters of the width reduction pressing device in addition to the parameters of the rough rolling mill 5 were used as the input data. The operational parameters of the width reduction pressing device used are the width reduction amount SPW, the feed pitch SPP, and the width reduction start position SPS. In the width prediction model No. 3, the operational parameters of the heating furnace 2 in addition to the parameters of the rough rolling mill 5 were used as the input data. The operational parameters of the heating furnace 2 used are the in-furnace time IFT, the extraction temperature ET, and the distance D1 with the furnace wall representing the loading position.

[0099]In the present example, the hyperparameters of the width prediction models No. 1 to 3 were 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 rough 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 rough 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 rough 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 the range to all the pieces of test data was calculated.

[0100]Table 1 shows the results of the prediction accuracy. In No. 1, the RMSE calculated from the deviation between the performance data W_a and the mean value W_m of the rough delivery-side width W was 1.0 mm. In addition, the probability that the rough delivery-side width W falls within a range of W_m±W_σ was 70.0%, which was close to the probability of 68.3% in a case where it was assumed that the variation in the rough delivery-side width W followed the normal distribution. In No. 2, the RMSE was 0.1 mm and the prediction accuracy was improved as compared with No. 1. On the other hand, the probability that the rough delivery-side width W falls within a range of W_m±W_σ was 66.3%, which was close to the probability of 68.3% in a case where it was assumed that the variation in the rough delivery-side width W followed the normal distribution. In No. 3, the RMSE was 0.0 mm, and high prediction accuracy was obtained for the mean value of the rough delivery-side width W. In addition, the probability that the rough delivery-side width W falls within a range of W_m±W_σ was 66.0%, which was close to the probability of 68.3% in a case where it was assumed that the variation in the rough delivery-side width W followed the normal distribution. From the above, it has been confirmed that any width prediction model can accurately predict the mean value Wm and the standard deviation W_σ of the rough delivery-side width as the statistical information of the rough delivery-side width.

[0101]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

[0102]According to the present invention, it is possible to provide the width prediction method of the rough-rolled material capable of predicting the statistical information including the variation in the width of the rough rolled material. In addition, according to the present invention, it is possible to provide the width control method of the rough rolled material capable of accurately controlling the width in the longitudinal direction of the rough rolled material in consideration of the variation in the width of the rough rolled material. In addition, according to the present invention, it is possible to provide the manufacturing method of the 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 the generation method of the width prediction model of the rough rolled material capable of generating the width prediction model that predicts the statistical information including the variation in the width of the rough rolled material.

REFERENCE SIGNS LIST