Method for predicting width of finish-rolled material, method for controlling width of finish-rolled material, method for manufacturing hot-rolled steel sheet, and method for generating model for predicting width of finish-rolled material

Abstract

This method for predicting the width of a finished product predicts the width of a finished product in a hot rolling line, the hot rolling line including a heating furnace for heating a slab, a roughing mill for roughing the heated slab to produce a roughed product, and a finishing mill for finishing the roughed product to produce a finished product. The method for predicting the width of the finish-rolled material includes a prediction step for predicting statistical information of the width of the finish-rolled material using a width prediction model learned by a Gaussian process regression method. The width prediction model includes, as input data, a set value or a measured value of the width of the rough rolled material and one or more operating parameters selected from among the operating parameters of the finishing mill, and takes statistical information of the width of the finish rolled material as output data.

Description

Technical Field

[0001] The present invention relates to a method for predicting the width of a finish-rolled workpiece in a hot rolling line, a method for controlling the width of a finish-rolled workpiece, a method for manufacturing a hot-rolled steel sheet, and a method for generating a width prediction model of a finish-rolled workpiece. Background Art

[0002] In a hot rolling line, first, a slab as a steel sheet material is heated by a heating furnace, the width of the slab is adjusted by a width-adjusting stamping device (finishing press), and a semi-finished steel sheet called a rough-rolled slab with a thickness of about 30 to 50 mm (hereinafter referred to as a rough-rolled workpiece) is manufactured by rough rolling using one or more than two roughing mills. Next, after cutting the front and rear ends of the rough-rolled workpiece by a crop shear, the rough-rolled workpiece is finish-rolled by a finishing mill composed of 5 to 7 rolling mill stands capable of continuous rolling to manufacture a steel sheet with a thickness of 1.0 to 25.0 mm (hereinafter referred to as a finish-rolled workpiece). And finally, the finish-rolled workpiece in a high-temperature state is cooled by a cooling device of an exit roller table and then wound by a coiler (winding machine) to become a hot-rolled steel sheet. In the hot rolling line, since plastic deformation is applied to the steel sheet in the thickness direction and the width direction in the width-adjusting stamping device, the roughing mill, and the finishing mill, the width of the steel sheet varies complexly 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 workpiece in the stage before the end of rough rolling and loading into the finishing mill is controlled (roughing width control), and the width of the steel sheet is controlled during the process through the finishing mill (finishing width control).

[0003] In the hot rolling line, the width of the steel sheet changes for various reasons, and thus various techniques for improving the width accuracy of the hot-rolled steel sheet have been proposed. For example, Patent Document 1 describes a method for controlling the width of a finish-rolled workpiece (hereinafter referred to as the finish-rolled output side width). Specifically, the method described in Patent Document 1 is to calculate the amount of change in the width of the steel sheet in the finishing mill, and control the opening degree of an edger provided on the input side of the roughing mill and / or the finishing mill based on the calculated value and the target value of the finish-rolled output side width, thereby controlling the finish-rolled output side width. And Patent Document 1 describes using a prediction formula with parameters such as the thickness of the steel sheet, the reduction ratio, the inter-stand tension, the change in the convexity ratio, the deformation resistance and temperature of the steel sheet, and the inter-stand passing time in each rolling mill stand to predict the amount of change in the width of the steel sheet in the finishing mill. In addition, the method described in Patent Document 1 calculates the prediction formula by dividing it into three regions: near the roll cutter inlet, inside the roll cutter, and between the rolling mill stands.

[0004] Moreover, Patent Document 2 also describes a method for controlling the width on the output side of finish rolling. In Patent Document 2, when using a prediction formula for predicting the amount of width change of a steel plate in a finish rolling mill, different formulas are applied as prediction formulas for width change near the roll cutter depending on whether the change in the crown ratio in each rolling mill stand is positive or negative. Patent Document 3 describes a method for correcting the target value of the width of a steel plate based on the deviation between the measured value of the width of the steel plate obtained at the initial stage of rolling and the target value when controlling the width on the output side of finish rolling. That is, the method described in Patent Document 3 is to obtain the actual data of the amount of width change of the steel plate during finish rolling at the initial stage of rolling and correct the target value of the width of the steel plate based on this actual data.

[0005] Prior Art Documents

[0006] Patent Documents

[0007] Patent Document 1: Japanese Patent Laid-Open No. 5-285516

[0008] Patent Document 2: Japanese Patent Laid-Open No. 8-112609

[0009] Patent Document 3: Japanese Patent Laid-Open No. 2006-51512

[0010] Non-Patent Document 1: "Gaussian Process and Machine Learning", by Daichi Mojibashi and Naruse Sei, published on March 7, 2019, ISBN 978-4-06-152926-7, Kodansha ("Gaussian Process and Machine Learning", by Daichi Mojibashi and Naruse Sei, published on March 7, 2019, ISBN 978-4-06-152926-7, Kodansha) Summary of the Invention

[0011] Technical Problem to be Solved by the Invention

[0012] However, in the method described in Patent Document 1, the predictive calculation used calculates a representative value of the width change amount of the steel plate in the finishing mill, rather than predicting the fluctuation of the width change amount of the steel plate. Therefore, according to the method described in Patent Document 1, due to reasons such as the temperature estimation error of the steel plate in finishing, it is inevitable that the width change amount of the steel plate fluctuates, and the width on the finishing output side becomes too small or too large. Also, the method described in Patent Document 2 similarly calculates a representative value of the width change amount of the steel plate in the finishing mill, rather than predicting the fluctuation of the width change amount of the steel plate. Therefore, it is inevitable that the width on the finishing output side becomes too small or too large. In contrast, the method described in Patent Document 3 determines the fluctuation of the width change amount of the steel plate in the finishing mill based on the measured data obtained at the initial stage of rolling. However, since the width change amount of the steel plate in the finishing mill varies with changes in operating conditions, there is still room for improvement in accurately predicting the fluctuation of the width change amount of the steel plate.

[0013] As described above, conventional finishing width control uses a strict physical model to predict the width change amount of the steel plate or determine the fluctuation of the width change amount of the steel plate obtained from the actual values, thereby making the width on the finishing output side highly accurate. However, regarding the width change amount of the steel plate in the finishing mill, it is inevitable that fluctuations occur due to various reasons. Therefore, there are cases where the width of the steel plate is too small and cases where the width of the steel plate is too large, inevitably resulting in poor width accuracy of the hot-rolled steel plate and a decrease in the product yield.

[0014] The present invention is made to solve the above technical problems, and its object is to provide a width prediction method for a finished rolled product that can predict statistical information including fluctuations in the width of the finished rolled product. Another object of the present invention is to provide a width control method for a finished rolled product that can consider fluctuations in the width of the finished rolled product and accurately control the width in the length direction of the finished rolled product. Another object of the present invention is to provide a manufacturing method for a hot-rolled steel plate that can improve the product yield of the hot-rolled steel plate. Another object of the present invention is to provide a method for generating a width prediction model for a finished rolled product that can generate a width prediction model for predicting statistical information including fluctuations in the width of the finished rolled product.

[0015] Technical solutions for solving technical problems

[0016] The width prediction method for the finish-rolled product of the present invention predicts the width of the finish-rolled product in a hot rolling line. The hot rolling line includes a heating furnace for heating a slab, a rough rolling mill for rough rolling the heated slab to produce a rough-rolled product, and a finish rolling mill for finish rolling the rough-rolled product to produce the finish-rolled product. The width prediction method for the finish-rolled product is characterized in that it includes a prediction step of using a width prediction model learned by the method of Gaussian process regression to predict the statistical information of the width of the finish-rolled product. The width prediction model includes, as input data, a set value or a measured value of the width of the rough-rolled product and one or more operation parameters selected from the operation parameters of the finish rolling mill, and takes the statistical information of the width of the finish-rolled product as output data.

[0017] Optionally, the width prediction model includes, as input data, one or more parameters selected from the attribute information of the slab.

[0018] The width control method for the finish-rolled product of the present invention includes a setting step of using the width prediction method for the finish-rolled product of the present invention to predict the statistical information of the width of the finish-rolled product, and setting one or more operation parameters selected from the operation parameters of the finish rolling mill based on the predicted statistical information in such a way that the probability that the width of the finish-rolled product is lower than the target width becomes smaller.

[0019] Optionally, the statistical information of the width of the finish-rolled product includes the average value W of the width of the finish-rolled product m and the standard deviation W σ , and the setting step includes setting one or more operation parameters selected from the operation parameters of the finish rolling mill in such a way that the target width W of the finish-rolled product t satisfies the relationship shown in the following mathematical formula (1).

[0020] [Formula 1]

[0021] W m - 2.5W σ ≦W t ≦W m - 1.5W σ ...(1)

[0022] The method for manufacturing a hot-rolled steel sheet of the present invention includes a step of manufacturing a hot-rolled steel sheet by using the width control method for the finish-rolled product of the present invention.

[0023] A method for generating a width prediction model for a finish-rolled product of the present invention generates a width prediction model for predicting the width of a finish-rolled product in a hot rolling line. The hot rolling line includes a heating furnace for heating a slab, a rough rolling mill for rough rolling the heated slab to produce a rough-rolled product, and a finish rolling mill for finish rolling the rough-rolled product to produce the finish-rolled product. The method for generating the width prediction model for the finish-rolled product is characterized in that it includes: a learning data acquisition step of acquiring a plurality of learning data, the plurality of learning data including performance data of a set value or a measured value of the width of the rough-rolled product, one or more pieces of operation performance data selected from the operation performance data of the finish rolling mill, and performance data of the width of the finish-rolled product; a step of generating the width prediction model by using the plurality of learning data acquired in the learning data acquisition step and using the method of Gaussian process regression. The width prediction model includes, as input performance data, performance data of a set value or a measured value of the width of the rough-rolled product, one or more pieces of operation performance data selected from the operation performance data of the finish rolling mill, and outputs statistical information on the width of the finish-rolled product.

[0024] Effects of the Invention

[0025] According to the width prediction method for a finish-rolled product of the present invention, it is possible to predict statistical information including fluctuations in the width of the finish-rolled product. Further, according to the width control method for a finish-rolled product of the present invention, it is possible to accurately control the width in the length direction of the finish-rolled product while considering fluctuations in the width of the finish-rolled product. Further, according to the method for manufacturing a hot-rolled steel sheet of the present invention, it is possible to improve the product yield of the hot-rolled steel sheet. Further, according to the method for generating a width prediction model for a finish-rolled product of the present invention, it is possible to generate a width prediction model for predicting statistical information including fluctuations in the width of the finish-rolled product. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a schematic diagram showing a structural example of a hot rolling line to which the present invention is applied.

[0027] Figure 2 is a diagram showing Figure 1 a structural example of the finish rolling mill shown.

[0028] Figure 3 is a diagram showing the composition of Figure 2 a structural example of one rolling mill stand of the finish rolling mill shown.

[0029] Figure 4 is used to illustrate the operation of a loop configured between the rolling mill stands of the finish rolling mill shown in Figure 2 a schematic diagram.

[0030] Figure 5 is a schematic diagram for explaining an optical width measurement method.

[0031] Figure 6 It is a flowchart showing the process of the model generation step of an embodiment of the present invention.

[0032] Figure 7 It is a flowchart showing the process of the prediction step of an embodiment of the present invention.

[0033] Figure 8 It is a block diagram showing the configuration of the width prediction model generation unit of an embodiment of the present invention.

[0034] Figure 9 It is a diagram for explaining the method of setting the control target width in the conventional width control method.

[0035] Figure 10 It is a block diagram showing the configuration of the width prediction unit of an embodiment of the present invention.

[0036] Figure 11 It is a diagram showing the relationship between the probability density distribution of the width on the finish rolling output side predicted by the width prediction model and the target width.

[0037] Figure 12 It is a diagram for explaining the method of setting the control target value of the finish rolling width control in this embodiment.

[0038] Figure 13 It is a diagram showing the relationship between the probability density distribution of the width on the finish rolling output side predicted by the width prediction model and the target width.

[0039] Figure 14 It is a diagram showing the relationship between the deviation of the width on the finish rolling output side from the target width and the cut-off amount of the steel plate. Detailed Embodiment

[0040] Hereinafter, with reference to the accompanying drawings, the width prediction method of the finish rolled product, the width control method of the finish rolled product, the manufacturing method of the hot rolled steel sheet, and the generation method of the width prediction model of the finish rolled product according to an embodiment of the present invention will be described in detail.

[0041] 〔Hot Rolling Line〕

[0042] First, with reference to Figures 1 to 5 the structure of the hot rolling line to which the present invention is applied will be described.

[0043] Figure 1 It is a schematic diagram showing an example of the structure of the hot rolling line to which the present invention is applied. As Figure 1As shown, the hot rolling line 1 to which the present invention is applied includes a heating furnace 2, a descaling device 3, a width adjusting and stamping 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 shown) is heated to a specified set temperature after being charged into the heating furnace 2 and is taken out of the heating furnace 2 as a hot slab. The hot slab taken out of the heating furnace 2 has the primary scale formed on its surface removed by the descaling device 3, and then the width is reduced to a specified set width by the width adjusting and stamping device 4. The slab with reduced width is rolled to a specified thickness in the rough rolling mill 5 to become a rough rolled product and is conveyed to the finish rolling mill 6. In the finish rolling mill 6, the rough rolled product is rolled to the product thickness by a continuous rolling mill composed of 5 to 7 rolling mill stands, thereby becoming a finish rolled product. On the downstream side of the finish rolling mill 6, a cooling device 7 is provided in a device called an exit roller table. The finish rolled product is wound into a coil shape by the coiler 8 after being cooled to a specified temperature.

[0044] Moreover, in the middle of the conveying process of the hot rolling line 1, a plurality of width gauges are provided as a width measuring unit. In Figure 1 the example shown, a rough rolling output side width gauge 11 is provided on the output side of the rough rolling mill 5, and a finish rolling output side width gauge 12 is provided on the output side of the finish rolling mill 6. Moreover, a coiler front width gauge (coiler input side width gauge) 13 for measuring the width of the finish rolled product before winding is provided on the output side of the cooling device 7. And a finish rolling input side width gauge 14 for measuring the width of the rough rolled product is provided on the input side of the finish rolling mill 6. However, if no unit for applying plastic deformation to the rough rolled product is provided between the rough rolling mill 5 and the finish rolling mill 6, the width of the rough rolled product measured by the rough rolling output side width gauge 11 is the same as the width of the rough rolled product measured by the finish rolling input side width gauge 14. In the present embodiment, sometimes the width of the rough rolled product measured by the rough rolling output side width gauge 11 is referred to as the rough rolling output side width, the width of the finish rolled product measured by the finish rolling output side width gauge 12 is referred to as the finish rolling output side width, and the width of the steel plate measured by the coiler front width gauge 13 is referred to as the coiler front width. And sometimes the width of the rough rolled product measured by the finish rolling input side width gauge 14 is referred to as the finish rolling input side width, but it can also be regarded as the same as the rough rolling output side width.

[0045] The hot rolling line 1 is equipped with a control controller (PLC) 90 for controlling each device constituting the hot rolling line 1, a control computer (process computer) 91 for applying control instructions to the control controller 90, and a host computer 92 for giving manufacturing instructions to the hot rolling line 1. The width control of the steel plate in the hot rolling line 1 is carried out in the following manner: the host computer 92 or the control computer 91 sets the control target values of the rough rolling output side width (rough rolling control target width), the finish rolling output side width (finish rolling control target width), and the width before the coiler (coiler front control target width) based on the manufacturing instructions from the host computer 92, and sets the operating conditions of the roughing mill 5 and the finishing mill 6. Specifically, the host computer 92 or the control computer 91 sets the target width of the finish rolled piece, that is, the finish rolling target width (hereinafter sometimes simply referred to as the target width) based on the coiler front target width (coiler front target width) determined according to the product specifications of the hot rolled steel plate, considering the width change amount of the steel plate generated between the output side of the finishing mill 6 and the width meter 13 before the coiler. Moreover, the host computer 92 or the control computer 91 sets the target width of the rough rolled piece (rough rolling target width) considering the width change amount of the steel plate in the finishing mill 6 based on the set finish rolling target width. In this case, the target values of the width control (rough rolling control target width, finish rolling control target width, coiler front control target width) are sometimes set by presetting a width margin (allowance) relative to the rough rolling target width, the finish rolling target width, and the coiler front target width. And the host computer 92 or the control computer 91 sets the rolling conditions in each pass of the rough rolling so that the rough rolling output side width is consistent with the rough rolling control target width. And the host computer 92 or the control computer 91 sets the rolling conditions in each rolling mill stand of the finish rolling so that the finish rolling output side width is consistent with the finish rolling control target width. Moreover, the host computer 92 or the control computer 91 sometimes sets the tension between the finishing mill 6 and the coiler 8 and the cooling conditions of the cooling device 7 so that the width before the coiler is consistent with the coiler front control target width. In this case, in the finishing mill 6, dynamic width control is sometimes performed while referring to the measured values of the rough rolling output side width and the finish rolling output side width. The control controller 90 has a function of collecting information obtained from various sensors (thickness gauge, thermometer, etc.) in addition to collecting information obtained from the width meters provided on the hot rolling line 1 at a specified sampling period and outputting them to the control computer 91 at the specified sampling period.

[0046] The width prediction method of the finish rolled piece according to an embodiment of the present invention is a method for predicting the finish rolling output side width. And the width control method of the finish rolled piece according to an embodiment of the present invention is a method for controlling the width of the steel plate so that the finish rolling output side width satisfies a specified relationship with respect to the finish rolling target width.

[0047] 〔Finishing mill〕

[0048] Figure 2 Yes means Figure 1 The schematic diagram of the structural example of the finishing mill 6 is shown in FIG. The rough rolled piece is conveyed to the entrance of the finishing mill 6. Figure 2 As shown in FIG. 1 , a head trimmer 61 is arranged at the entrance of the finishing mill 6. The head trimmer 61 is a device for cutting and removing the head trimmers (the deformed shape of the front and rear ends of the rough rolled piece) formed at the front and rear ends of the rough rolled piece. As a result, the rough rolled piece is shaped into a substantially rectangular plane shape that can be easily and smoothly gripped by the finishing mill 6. Hereinafter, the rough rolled piece SA loaded into the finishing mill 6 will be referred to as a steel plate SB. Figure 2 The finishing mill 6 shown is composed of 7 rolling mill stands F1 to F7, but the number of rolling mill stands is not limited to this. Usually, the number of rolling mill stands of the finishing mill 6 is 6 to 7, and sometimes it is composed of 5 rolling mill stands. The finishing mill 6 is a hot tandem finishing mill that uses a plurality of rolling mill stands to simultaneously roll the steel sheet SB at a temperature set in the range of 800 to 1100° C. according to the steel type, and is abbreviated and simply referred to as a “finishing mill”.

[0049] Figure 3 (a) and (b) represent the composition Figure 2 FIG. 6 is a schematic diagram of a structural example of a rolling mill stand of a finishing mill 6. Figure 3 As shown in (a) and (b), the rolling mill frame has a structure in which a pair of workpiece rollers 62a and 62b are provided above and below the rolling line of the steel plate SB. The workpiece rollers 62a and 62b are supported by support rollers 63a and 63b, respectively. The rolling load applied to the steel plate SB is transmitted to the housing 65 via the bearings (support roller supports) 64a and 64b of the support rollers 63a and 63b. A load sensor 66 as a load detector may be arranged between the housing 65 and the support roller support 64b, and the rolling load applied to the steel plate SB is measured by the load sensor 66. In addition, the upper support roller support 64a and the housing 65 may be connected via a lower pressure cylinder 67, and the lower pressure cylinder 67 adjusts the opening (roller gap) between the pair of workpiece rollers 62a and 62b by adjusting the position of the pair of workpiece rollers 62a and 62b in the up-down direction.

[0050] The rolling mill stands F1 to F7 that make up the finishing mill 6 are equipped with shape control actuators for controlling the profile (thickness distribution in the width direction of the steel sheet SB) and flatness of the steel sheet SB. The shape control actuator is a mechanism for adjusting the roll gap distribution between a pair of work rolls 62a and 62b. A representative example of the shape control actuator is a work roll bender. The work roll bender is equipped with a hydraulic device (not shown) that applies a force between the bearing boxes (work roll supports) 68a and 68b at both ends of each of the pair of work rolls 62a and 62b. The hydraulic device applies a bending force to the pair of work rolls 62a and 62b by applying a force between the upper and lower work roll supports 68a and 68b, and adjusts the roll gap distribution by applying a flexural deformation to the pair of work rolls 62a and 62b. At this time, the force applied between the upper and lower work roll supports 68a and 68b is called the bending force. And, in the rolling mill stands F1 to F7, as the shape control actuator, in most cases, other shape control actuators are provided in addition to the work roll bender. For example, in the case of a paired cross rolling mill, the upper work roll 62a and the upper backup roll 63a are set as a group, and are inclined (crossed) in the horizontal plane with respect to the lower work roll 62b and the lower backup roll 63b, thereby adjusting the roll gap distribution. In this case, the angle formed by the upper and lower rolls is called the crossing angle, and the roll gap distribution changes by changing the crossing angle. And, as the shape control actuator, a work roll shifter that shifts a pair of work rolls 62a and 62b in opposite directions relative to the axial direction can also be used. Moreover, in the case of a rolling mill with a six-stage rolling mill stand, an intermediate roll shifter that shifts the upper and lower intermediate rolls in opposite directions relative to the axial direction of the rolls is used. The shape control actuator provided in the rolling mill stand adjusts the crown ratio of the steel sheet SB by adjusting the distribution of the roll gap, thereby enabling adjustment of the width of the steel sheet SB.

[0051] Figure 4 It is used to explain the operation of the loop configured between the rolling mill stands F1 to F7 of the finishing mill 6 shown in Figure 2 the schematic diagram. Figure 4The loop 69 shown is a device for adjusting the balance between the conveying speed of the steel plate SB carried out from the rolling mill stand Fi on the upstream side and the conveying speed of the steel plate SB loaded into the rolling mill stand Fi+1 on the downstream side. The loop 69 includes a loop roll 69a whose front end contacts the steel plate SB. The loop 69 controls the loop angle Lθ and the loop height LH such that the inter-stand tension applied to the steel plate SB between the rolling mill stand Fi and the rolling mill stand Fi+1 is within a specified range. Also, the circumferential speed of the work roll of the rolling mill stand Fi on the upstream side is controlled such that the loop height LH is within a specified range. In this case, the inter-stand tension can also be measured using a load detector disposed on the loop roll 69a. Also, the inter-stand tension can be estimated based on the torque applied to the motor for driving the loop 69. Anyway, the width of the steel plate SB varies according to the inter-stand tension, so the inter-stand tension applied to the steel plate SB between the rolling mill stands in the finishing mill 6 is measured.

[0052] 〔Width meter〕

[0053] Return to Figure 1 The width of the steel plate in the hot rolling line 1 is measured by a rough rolling output side width meter 11, a finishing rolling output side width meter 12, a width meter 13 before the coiler, and a finishing rolling input side width meter 14. Most of these width meters use an optical width measurement method. The optical width measurement method is to dispose a light source below the rolling path for conveying the steel plate and an image sensor above, and measure the width of the steel plate based on the shadow length in the width direction of the light emitted from the light source during the passage of the steel plate. Also, the width meter can measure the width by determining the positions of the width direction ends of the steel plate with a camera. Figure 5 (a) and (b) are schematic views showing a structural example of the rough rolling output side width meter using a camera. In Figure 5 the example shown in (a), a set of cameras 16a, 16b provided in the rough rolling output side width meter capture an image of the steel plate SB including the width direction ends of the steel plate SB. The cameras 16a, 16b use CMOS or CCD sensors. Also, the image processing unit provided in the rough rolling output side width meter determines the positions of the width direction ends of the steel plate SB based on the images captured by the cameras 16a, 16b, and calculates the width W of the steel plate SB based on the installation interval of the cameras 16a, 16b. The reference numeral 15 in the figure represents the rolling path. However, since this width meter captures the width direction ends of the steel plate SB obliquely, it is easy to generate a width measurement error when the steel plate SB floats from the rolling path 15. Therefore, the width meter mostly has a function of correcting the width measurement error corresponding to the floating of the steel plate SB from the rolling path. Specifically, as Figure 5As shown in (b), when the steel plate SB is conveyed at a height of the lifting amount H from the rolling line 15, the measurement error of the width is corrected as follows. That is, first, a set of cameras 16a and 16b arranged in the width direction of the steel plate SB determine the both end portions in the width direction of the steel plate SB, thereby determining the measured value W1 of the width. Next, another set of cameras 16c and 16d arranged in the width direction of the steel plate SB also determine the both end portions in the width direction of the steel plate SB, thereby determining the measured value W2 of the width. Then, based on the positional relationship between the two sets of cameras (in the example shown in Figure 5 (b), the interval D in the width direction between the cameras 16a and 16b and the interval L in the width direction between the camera 16a (16b) and the camera 16c (16d)), the actual width W of the steel plate SB is calculated by the following mathematical formula (2), and it becomes the measured value of the width of the steel plate SB.

[0054] [Formula 2]

[0055]

[0056] However, as another method for measuring the width, the following method is also used: Laser is emitted in the width direction of the steel plate, the reflected light from the end face of the steel plate is received, and the width of the steel plate is measured based on the distances to the both end faces of the steel plate. The width meter also has a thermal expansion correction function for converting into the width of the cooled steel plate based on the temperature of the steel plate. The width of the steel plate is measured by the width meter during the conveyance of the steel plate, so the measured value of the width of the steel plate obtained by the width meter is time-series numerical information corresponding to the sampling interval of the width meter. And, using the information of the conveyance speed at the position where the steel plate passes through the width meter, it is converted into the relationship between the position in the length direction of the steel plate and the actual value of the width of the steel plate. And, in the control computer 91, the representative value of the width of the steel plate is calculated based on the measured value of the width of the steel plate obtained. The representative value of the width of the steel plate can use the average value (average width) of the width of the steel plate in the length direction of the steel plate, the measured value (stable width) of the width of the steel plate in the stable portion except for the front and rear end portions of the steel plate, the measured value (front width) of the width of the steel plate in the front end portion of the steel plate, the measured value (tail width) of the width of the steel plate in the tail end portion of the steel plate, etc. And, sometimes the minimum value (minimum width) and the maximum value (maximum width) of the width of the steel plate in the length direction of the steel plate are calculated, etc. The measured value of the width of the steel plate measured by the width meter is also sometimes expressed by the deviation from the preset target width.

[0057] 〔Gaussian process regression〕

[0058] The width prediction method for the finish-rolled product according to an embodiment of the present invention is a method for predicting the width on the output side of the finish rolling on the hot rolling line 1 described above. The width prediction method for the finish-rolled product according to an embodiment of the present invention uses a width prediction model learned by the method of Gaussian process regression. The method of Gaussian process regression includes, as input data, a set value or a measured value of the width of the rough-rolled product and one or more operation parameters selected from the operation parameters of the finishing mill 6, and uses the statistical information of the width on the output side of the finish rolling as output data. Hereinafter, the method of Gaussian process regression applied in the width prediction method for the finish-rolled product according to an embodiment of the present invention will be described.

[0059] Gaussian process regression, also known as Gaussian process regression and Gaussian process, etc., is a type of non-linear regression model for estimating a function from input variables to output variables. The output can be set as a probability distribution. When using a Gaussian distribution determined by two parameters, namely the mean and the variance, it is called a Gaussian process. The method of Bayesian estimation is used to obtain the probability distribution, indicating the reliability and uncertainty of the estimation. For example, when m variables are selected as the input of the width prediction model, the input variables are represented by the input vector x. And the output variable corresponding to the input vector x as the learning data is set as y. Hereinafter, a method of using n learning data x (1) ~x (n) 、y (1) ~y (n) and obtaining the statistical information y ＊ of the width on the output side of the finish rolling corresponding to the new input vector x ＊ by the method of Gaussian process regression will be specifically described. The m variables constituting the input vector x each represent different physical quantities, so the m variables can also be standardized (normalized) in advance. Specifically, for each of the m variables, the mean value and the standard deviation can be calculated based on the n learning data, and the calculated mean value and standard deviation are used to standardize each variable. This is because the learning efficiency of the hyperparameters described later can be improved by standardizing the m variables in advance. In this case, in order to convert the m variables into physical quantities, only the inverse transformation needs to be performed using the calculated mean value and standard deviation.

[0060] In Gaussian process regression, a probability model is used in which a function f(x) representing the output variable y is estimated based on the input variable x and added with Gaussian noise. For example, the probability model is represented by the following mathematical formula (3). In this case, it is assumed that the function f(x) follows a multivariate Gaussian distribution. And it is assumed that the Gaussian noise ε (i) follows a Gaussian distribution with a mean of zero and a variance of σ e (i)2 . However, the Gaussian noise ε (i) can also be set to depend on the n learning data x(1) ~x (n) value, and can also be a constant noise independent of the n learning data x (1) ~x (n) instead of being a constant noise

[0061] [Equation 3]

[0062] y (i) = f(x (i) + ∈ (i) …(3)

[0063] The Gaussian distribution refers to a distribution in which the probability density N is represented by the following mathematical formula (4). In the mathematical formula (4), μ represents the mean value, and σ represents the standard deviation (σ 2 represents the variance). That is, the Gaussian distribution is a probability density determined by the mean value μ and the standard deviation σ or the variance σ 2 Gaussian process regression uses a multivariate normal distribution that extends this Gaussian distribution to multiple dimensions

[0064] [Equation 4]

[0065]

[0066] In Gaussian process regression, the mean function (mean vector) representing the multivariate Gaussian distribution is set to a constant (for example, zero), and the covariance matrix is represented by a kernel function. The kernel function is a function used to calculate the similarity of data. The kernel function uses the input vectors x (i) , x (j) as independent variables and is expressed as k(x (i) , x (j) ), and outputs the similarity between the input vector x (i) and the input vector x (j) . As the kernel function, well-known kernel functions such as the white kernel function, linear kernel function, polynomial kernel function, Gaussian kernel function, and Matern kernel function can be used. If several kernel functions are exemplified, they are represented by using the parameter θ as shown in the following mathematical formulas (5) to (7). The mathematical formula (5) represents the linear kernel function, the mathematical formula (6) represents the quadratic polynomial kernel function, and the mathematical formula (7) represents the Gaussian kernel function

[0067] [Equation 5]

[0068] k(x (i) , x (j) ) = θ · x (i) · x (j)T …(5)

[0069] [Equation 6]

[0070] k(x (i) , x (j) ) = (1 + θ · x(i) ·x (j)T ) 2 …(6)

[0071] [Equation 7]

[0072] k(x (i) ,x (j) ) = exp(-(x (i) -x (j) ) 2 / θ)…(7)

[0073] Under the above assumptions, the function f(x) that represents the output variable y based on the input variable x is expressed as the following mathematical formula (8) using the probability density N.

[0074] [Equation 8]

[0075]

[0076] In this case, when the Gaussian noise is a constant value σ independent of the learning data e 2 , the covariance matrix K determined by the kernel function and the covariance matrix Σ that includes the Gaussian noise n are defined using the following mathematical formulas (9) and (10). n When this is the case, mathematical formula (8) is expressed as the following mathematical formula (11) or mathematical formula (12). Here, I represents the identity matrix.

[0077] [Equation 9]

[0078]

[0079] [Equation 10]

[0080]

[0081] [Equation 11]

[0082] y (i) = N(0, K n + σ e 2 I)…(11)

[0083] [Equation 12]

[0084] y (i) = N(0, ∑ n )…(12)

[0085] The covariance matrices K n , Σ n included in the right sides of mathematical formulas (11) and (12) include the learning data x (1) as input.~x (n) , the left sides of mathematical formulas (11) and (12) include the learning data y as the output (1) ~y (n) . Therefore, as long as the hyperparameters (parameters θ and Gaussian noise σ e 2 ) included in the kernel function are determined in such a way that the relationships shown in mathematical formula (11) or mathematical formula (12) hold. As a method for determining the hyperparameters, any method selected from well-known methods can be used. For example, the likelihood function of the learning data can be calculated, and the hyperparameters can be calculated by maximizing the log-likelihood represented by the logarithm of the calculated likelihood function. In this case, as a calculation method for maximizing the log-likelihood, optimization methods such as the Monte Carlo method and the conjugate gradient method can be used. Also, methods such as cross-validation and maximizing the marginal likelihood can be used.

[0086] Next, a method for estimating the statistical information y of the width on the finish rolling output side corresponding to a new input vector x ＊ using the function f(x) for which the hyperparameters of the kernel function have been determined will be described. The estimated value corresponding to the unknown input vector x ＊ not included in the learning data can be obtained by applying Bayesian estimation and expressed as the following mathematical formula (13). In this case, the vector of the newly determined kernel function k ＊ is defined as the following mathematical formula (14). ＊ is defined as the following mathematical formula (14).

[0087] [Equation 13]

[0088]

[0089] [Equation 14]

[0090]

[0091] Accordingly, mathematical formula (13) can be expressed as the following mathematical formula (15). Also, for the statistical information corresponding to the input vector x ＊ , the mean can be set to W m and the variance can be set to W σ and calculated by the following mathematical formulas (16) and (17). For the details of the method of Gaussian process regression, reference can be made to well-known literature (such as Non-Patent Document 1), etc.

[0092] [Equation 15]

[0093]

[0094] [Equation 16]

[0095]

[0096] [Equation 17]

[0097]

[0098] In the present embodiment, the step of determining hyperparameters for representing the relationship of the above-described mathematical formula (11) or mathematical formula (12) is referred to as a model generation step. Specifically, in the model generation step, as shown in Figure 6 , first, n learning data x (1) ~x (n) , y (1) ~y (n) (step S1) are obtained from the data set accumulated in a database or the like. Next, a kernel function used in machine learning is selected from, for example, mathematical formulas (5) to (7) (step S2). Next, as the Gaussian noise ε(i), a Gaussian distribution with an average value of zero and a variance of σ e 2 is set (step S3). Next, the covariance matrices K n , Σ n determined by the kernel function are calculated using mathematical formulas (9) and (10) (step S4). Then, the parameters θ and the Gaussian noise σ e as hyperparameters are determined by using mathematical formulas (11) and (12) representing the relationship between the input and output of the learning data and by a learning method using a likelihood function (step S5). The kernel function representing the input-output relationship of the learning data is determined by the hyperparameters thus determined. The determined hyperparameters may also be stored in the storage device of the computer that executes the model generation step. On the other hand, the step of calculating the average value W ＊ and the standard deviation W m as statistical information corresponding to the input vector x σ by using the hyperparameters determined by the model generation step is referred to as a prediction step. Specifically, in the prediction step, as shown in Figure 7 , first, a new input vector x ＊ (step S11) is obtained. Next, the hyperparameters stored in the storage device of the computer that executes the model generation step are obtained, and the kernel function k ＊ corresponding to the new input vector x ＊ is determined using mathematical formula (14) (step S12). Then, using the relationships shown in mathematical formulas (16) and (17), the predicted value corresponding to the input vector x ＊ is calculated as the average value W m and the standard deviation W σ (step S13).

[0099] [Method for Generating Width Prediction Model]

[0100] Next, as a method for generating a width prediction model for finish-rolled products, which is an embodiment of the present invention, an embodiment applying the above-described Gaussian process regression method will be described.

[0101] Figure 8 is a block diagram showing the configuration of a width prediction model generation unit according to an embodiment of the present invention. As Figure 8 shown, the width prediction model generation unit 100 of the present embodiment includes a database unit 101 and a machine learning unit 102. The database unit 101 stores a set value or actual value of the width on the rough rolling output side, one or more operation actual data selected from the operation actual data of the finishing mill 6, and actual data of the width on the finishing rolling output side. The database unit 101 may also store, as needed, one or more actual data selected from the actual data of the slab attribute information. Specific actual data stored in the database unit 101 will be described later.

[0102] The actual data stored in the database unit 101 can be appropriately obtained from the control controller 90, the control computer 91, or the host computer 92. Further, a data acquisition unit 103 may be provided to collect these actual data. The actual data is temporarily stored in the data acquisition unit 103, and after generating a data set in which various actual data are correlated, it is stored in the database unit 101. Since the timings at which the data stored in the database unit 101 are obtained are sometimes different, it is easy to construct a data set in which the data are in a corresponding relationship with each other by correlating various actual data in the data acquisition unit 103. Regarding the data set stored in the database unit 101, at least one actual data is obtained for one steel plate manufactured from one slab. For example, when using the average width of the finish-rolled product as the actual data of the width on the finishing rolling output side, the operation actual data of the finishing mill 6 may use the representative value as the actual data. In this case, regarding the width data of the finish-rolled product, the representative value of the finish-rolled product may be used, but the set value or measured value of the width at multiple positions along the length direction of the finish-rolled product may also be used. Regarding the actual data of the slab attribute information, the representative value corresponding to one steel plate may be used as the actual data.

[0103] On the other hand, in the data acquisition unit 103, for one steel plate manufactured from one slab, multiple data sets can also be generated and stored in the database unit 101. For example, when actual width data at the front end, stable part, and tail end of the finish-rolled product is acquired as actual width data on the finish-rolled output side, for the actual operation data of the finishing mill 6, the actual operation data respectively acquired at the front end, stable part, and tail end of the finish-rolled product can be associated with the actual width data on the finish-rolled output side at the corresponding positions. However, for actual width data such as the attribute information of the slab, which is determined regardless of the position in the length direction of the steel plate, the actual width data with the same attribute information is associated with the actual width data on the finish-rolled output side at the front end, stable part, and tail end of the steel plate.

[0104] Moreover, in the data acquisition unit 103, the actual width data on the finish-rolled output side can also be acquired for each position divided in the length direction with respect to one steel plate, and the actual operation data acquired for each position in the length direction of the steel plate is associated with the actual width data on the finish-rolled output side measured at each position and stored in the database unit 101. That is, the number of divisions in the length direction of the steel plate is set to, for example, about 20 to 200, and the actual width data on the finish-rolled output side within each division interval is associated with the actual operation data corresponding to each position. In this case, although the length of the steel plate SB rolled by the finishing mill 6 varies according to each rough rolling pass, as long as the actual operation data at the positions corresponding to the divisions in the length direction of the steel plate SB is acquired, data sets corresponding to each division interval can be formed in the data acquisition unit 103. When data sets corresponding to multiple positions divided in the length direction of the steel plate are stored in the database unit 101, a width prediction model that varies according to each position in the length direction of the steel plate can also be generated in the machine learning unit 102.

[0105] The width prediction model generation unit 100 can be provided in the control computer 91 for controlling the manufacture of the steel plate based on the hot rolling line 1. Moreover, the width prediction model generation unit 100 can also be provided in the host computer 92 that gives the manufacturing instruction to the control computer 91, or can also be provided in an independent computer capable of communicating with other devices. Also, the machine learning unit 102 can be configured as a device different from the database unit 101 using a device capable of receiving the data sets stored in the database unit 101. More than 100 data sets are stored in the database unit 101. It is also possible to store preferably more than 10,000, and more preferably more than 100,000 data sets in the database unit 101. The data stored in the database unit 101 is sometimes screened as needed.

[0106] The machine learning unit 102 uses the data sets stored in the database unit 101 and performs machine learning by a method based on Gaussian process regression to generate a width prediction model M. The learning data used by the machine learning unit 102 is multiple data sets including actual data containing the set value or actual value of the width on the rough rolling output side, one or more operation actual data selected from the operation actual data of the finishing mill 6, and the actual data of the width on the finishing rolling output side, stored in the database unit 101. The machine learning unit 102 uses those learning data to perform machine learning by the method of Gaussian process regression and generate the width prediction model M. In the method of Gaussian process regression, as the input actual data, it includes the actual data containing the set value or actual value of the width on the rough rolling output side, one or more operation actual data selected from the operation actual data of the finishing mill 6, and uses the statistical information of the width on the finishing rolling output side as the output data. Moreover, the machine learning unit 102 may also use the data sets stored in the database unit 101, use the actual data of the attribute information of the slab SA as the input actual data, perform machine learning by the method of Gaussian process regression, and generate the width prediction model M.

[0107] The machine learning in this case refers to determining the hyperparameters applied in the Gaussian process regression through Figure 6 the steps shown. And the width prediction model M refers to the hyperparameters determined in this way. This is because by determining the hyperparameters, the input-output relationship of the learning data is determined, so that the statistical information of the width on the finishing rolling output side corresponding to the unknown input can be predicted. And in the present embodiment, the statistical information of the width on the finishing rolling output side as the output of the width prediction model M learned by Gaussian process regression includes the prediction result of the average value of the width of the finished rolled piece and the index indicating its fluctuation, i.e., the standard deviation or variance. Thus, it is possible to predict the average value of the width on the finishing rolling output side and at the same time predict its fluctuation.

[0108] On the other hand, in the prior art, as described in Patent Documents 1 and 2 for example, a prediction formula for predicting the width change amount of the steel plate in the finishing rolling is used to predict the average value or representative value of the width on the finishing rolling output side and the width change amount of the steel plate in the finishing mill, but information related to its fluctuation cannot be obtained. Therefore, it is necessary to add a pre-set extra width (margin) to set the target value of the width of the steel plate. Specifically, the conventional width control method is as Figure 9 shown, with respect to the target width W t an extra width (margin) W r is pre-set, and the sum of the target width W t and the extra width W r is set as the control target width W c of the width on the finishing rolling output side. The extra width W rThe reason is that since there is a certain fluctuation in the width on the finishing mill output side, it is necessary to prevent the width on the finishing mill output side from being lower than the target width W. t If the width on the finishing mill output side is lower than the target width W t , the width of the hot-rolled steel plate may sometimes be lower than the product target width, and the product cannot be picked up due to insufficient width. Therefore, the manufactured hot-rolled steel plate is used as scrap or the delivery destination of the product is changed, etc., which sometimes leads to a decrease in the product yield rate and a delay in delivery. On the other hand, if the set excess width W r is too large, the width of the hot-rolled steel plate becomes too large compared to the product target width. Therefore, in order to obtain the product, trimming of the steel plate is required, resulting in a decrease in the product yield rate. That is, as a hot-rolled steel plate, if the occurrence of insufficient width is to be prevented, the width on the finishing mill output side becomes too large, and if the decrease in the yield rate caused by trimming is to be suppressed, insufficient width is likely to occur. Therefore, in the prior art, actual data of the width on the finishing mill output side and the width change amount in the finishing mill 6 are collected according to the thickness and width division of the hot-rolled steel plate, and the excess width is preset according to its fluctuation. The factory supervisor regularly monitors whether the setting of the excess width is appropriate.

[0109] In contrast, according to the present embodiment, the average value and statistical fluctuation of the width on the finishing mill output side are predicted based on the operating conditions of the hot rolling line as input. Therefore, it is possible to set an appropriate excess width not according to the thickness and width division of the hot-rolled steel plate as in the prior art, but according to the operating conditions for each steel plate. Thereby, it is possible to suppress a decrease in the product yield rate caused by insufficient width and width surplus of the hot-rolled steel plate due to the fluctuation of the width on the finishing mill output side.

[0110] 〔Attribute information of the slab〕

[0111] The attribute information of the slab that can be used in the input of the width prediction model M refers to the information related to the slab size and the information related to the composition of the slab that affect the width change of the steel plate in the finishing mill 6. The information related to the slab size is the information related to the thickness, width, length, and weight of the slab. The information related to the composition of the slab is the information related to the content of the components contained in the slab, and examples include the C content, Si content, Mn content, P content, S content, Nb content, Ti content, Cu content, Ni content, Mo content, B content, etc. of the slab. The information related to the slab size affects the temperature change of the steel plate in the hot rolling line 1, and thus affects the fluctuation of the width on the finishing output side. Moreover, the information related to the composition of the slab affects the deformation resistance of the steel plate and the composition and thickness of the oxide film formed on the surface of the steel plate. As a result, the frictional force at the interface between the roll and the steel plate is affected, the deformation state of the steel plate changes, and thus the fluctuation of the width on the finishing output side is affected. In addition, the information related to the composition of the slab affects the behavior of short-term creep deformation between the rolling mill stands of the finishing mill 6. As a result, the width reduction in the finishing mill 6 is affected, and the fluctuation of the width on the finishing output side is affected.

[0112] 〔Width data of the rough-rolled piece〕

[0113] The width data of the rough-rolled piece (the set value or measured value of the width of the rough-rolled piece) used in the input of the width prediction model M is the set value or measured value related to the width of the rough-rolled piece loaded into the finishing mill 6. The set value related to the width of the rough-rolled piece can use the representative value related to the width of the rough-rolled piece used in the setting calculation for controlling the operating conditions of the roughing mill 5 or the finishing mill 6 by the control computer 91. Moreover, when roughing, when the control computer 91 sets the target width and the control target width of the width of the rough-rolled piece on the output side of the roughing mill 5, these can be set as the width data of the rough-rolled piece. In addition, the control computer 91 uses the width of the rough-rolled piece on the input side of the finishing mill 6 to perform setting calculations before finishing, and the set value of the width on the finishing input side used at this time can also be set as the width data of the rough-rolled piece. On the other hand, the measured value related to the width of the rough-rolled piece can use the actual value of the width on the roughing output side measured by the roughing output side width meter 11. Moreover, the actual value of the width on the finishing input side measured by the finishing input side width meter 14 can be used. The measured values of the width of the rough-rolled piece measured by the roughing output side width meter 11 and the finishing input side width meter 14 are transmitted from the control controller 90 to the control computer 91, so that these values can be obtained from the control computer 91 by the data acquisition unit 103.

[0114] 〔Operating parameters of the finishing mill〕

[0115] The operating parameters of the finishing mill 6 used in the input of the width prediction model M refer to the rolling operation conditions that affect the width of the steel sheet in any rolling mill stand of the finishing mill 6. The operating parameters of the finishing mill 6 can use the operating parameters that affect the width of the steel sheet in three regions: near the roll entry corresponding to each rolling mill stand of the finishing mill 6, inside the roll cutter, and between the rolling mill stands. Specifically, the thickness, reduction ratio, inter-stand tension, change in crown ratio, deformation resistance, and temperature of the steel sheet in each rolling mill stand can be used. Also, the rolling load, roll opening, and work roll diameter of each rolling mill stand that indirectly affect the thickness and temperature of the steel sheet in each rolling mill stand can be used as operating parameters. Moreover, the set value or actual value of the shape control actuator that indirectly affects the change in the crown ratio of the steel sheet in each rolling mill stand can be used. For example, the set value and actual value of the actuator such as the bending force of the work roll bender, the crossing angle in the paired crossing mill, and the intermediate roll shift amount in the six-high mill, which are used to change the deflection of the work roll and control the profile of the steel sheet, can be used. In addition to these, the operating parameters of the finishing mill 6 can also use the operating parameters related to the speed of the steel sheet, such as the rolling speed, acceleration rate, rolling time, circumferential speed of the work roll of each rolling mill stand, and inter-stand passing time. This is because it affects the temperature change and deformation resistance of the steel sheet, and thus affects the width change amount of the steel sheet. Also, it affects the short-term creep deformation of the steel sheet, thereby affecting the width reduction between the rolling mill stands. Moreover, the operating parameters of the finishing mill 6 can also use the rolling length and usage time starting from the recombination of the work rolls used in each rolling mill stand. This is because the surface state of the work roll changes over time, and the friction state with the steel sheet changes, affecting the width expansion during rolling.

[0116] 〔Width prediction method for finish-rolled products〕

[0117] The width prediction method for finish-rolled products according to an embodiment of the present invention includes a prediction step of predicting the statistical information of the width on the finish-rolled output side using the width prediction model M generated as described above. The width prediction unit that executes the prediction step can be provided in the control computer 91 for controlling the hot rolling line 1. Also, the width prediction unit can be provided in the host computer 92 that gives manufacturing instructions to the control computer 91, or can be provided in an independent computer capable of communicating with other devices. Hereinafter, refer to Figure 10 The operation of the width prediction unit according to an embodiment of the present invention will be described.

[0118] Figure 10The operation of the width prediction unit 110 shown is performed on the steel plate manufactured in the hot rolling line 1 before the width at the finish rolling output side is measured by the finish rolling output side width gauge 12. The operation of the width prediction unit 110 can be performed, for example, at the stage of charging the steel plate to be predicted as a slab into the heating furnace 2 and at the stage of discharging from the heating furnace 2. At the stage of charging the slab into the heating furnace 2, information related to the slab size and the component composition of the slab, which is the attribute information of the slab, is determined by the host computer 92. And this is because at the stage of charging the slab into the heating furnace 2, the manufacturing specifications of the hot rolled steel plate are preset, and the corresponding standard operating parameters are determined. Therefore, the prediction step can be performed by using the actual data of the attribute information of the slab and the set values of other operating parameters determined as the standard operating parameters corresponding to the manufacturing specifications as inputs. And the prediction step can also be performed, for example, in the middle of the rolling pass of the rough rolled piece by the roughing mill 5. In rough rolling, the rough rolling width control in the roughing mill 5 is performed, and the target width and the control target width for the rough rolling output side width are set. Therefore, these set values can be used as inputs to the width prediction model M.

[0119] Moreover, the prediction step can be performed after the rough rolling is completed and before the rough rolled piece is charged into the finish rolling mill 6. Since the rough rolling is completed, the measured value of the width of the rough rolled piece can be obtained, and these actual values can be used as inputs to the width prediction model M. And the width at the rough rolling output side is measured by the rough rolling output side width gauge 11 and the finish rolling input side width gauge 14. Thus, the control computer 91 performs the setting calculation of the finish rolling mill 6 based on the measured value of the width at the rough rolling output side and sets the operating conditions of the finish rolling mill 6. Therefore, the operating parameters of the finish rolling mill 6 set by the setting calculation can be used as inputs to the width prediction model M. The prediction step can be performed at any time after the front end of the rough rolled piece is charged into the finish rolling mill 6 and before the tail end of the rough rolled piece passes through the finish rolling mill 6. In this case, the actual value of the operating parameters of the finish rolling mill 6 at the current time can be obtained, so the operating parameters of the finish rolling mill at the current time can be used as inputs to the width prediction model M. Thereby, the width at the finish rolling output side when the rough rolled piece to be charged into the rolling stand F1 of the finish rolling mill 6 is discharged from the rolling stand F7 can be predicted.

[0120] Figure 10 The input data acquisition unit 111 of the width prediction unit 110 shown acquires the actual values or set values of the operating parameters of the hot rolling line 1 held by the control computer 91 or the host computer 92 as described above. And the width prediction unit 110 inputs the input data acquired by the input data acquisition unit 111 to the prediction unit 112. The prediction unit 112 acquires the hyperparameters determined by the width prediction model generation unit 100, such as Figure 7Calculate the kernel function with respect to the input data (new output vector) as shown, and calculate the statistical information of the width on the finish rolling output side as the output data. As described above, the operation of the width prediction unit 110 can be executed at any time during the period until the tail end of the steel plate passes through the finish rolling mill 6, so it can also be executed multiple times during the process of manufacturing one steel plate. The statistical information of the width on the finish rolling output side output as above can also be displayed on a monitor or the like connected to the width prediction unit 110. By resetting the operation parameters of the finish rolling mill 6 based on the output display of the statistical information of the width on the finish rolling output side, the generation of width defects in the hot-rolled steel plate can be suppressed.

[0121] 〔Width control method for finish rolled products〕

[0122] The width control method for finish rolled products according to an embodiment of the present invention is based on the statistical information of the width on the finish rolling output side predicted as described above, and when the width on the finish rolling output side is lower than the target width (target width) W of the finish rolled product t Reset one or more operation parameters selected from the operation parameters of the finish rolling mill 6 in such a way that the probability becomes smaller. In the above-mentioned width prediction method for finish rolled products, the output of the width prediction model M, that is, the statistical information of the width on the finish rolling output side, is determined as, for example, the average value W of the width on the finish rolling output side m and the standard deviation W σ In this case, it is predicted that the width W on the finish rolling output side follows the probability density distribution g(W) shown in the following mathematical formula (18).

[0123] [Equation 18]

[0124]

[0125] Figure 11 is an example schematically showing the probability density distribution g(W) of the width on the finish rolling output side predicted by the width prediction model M together with the target width W t In Figure 11 , according to the average value W of the width W on the finish rolling output side predicted by the width prediction model M m is smaller than the target width W t and the fluctuation of the width W on the finish rolling output side, it is predicted that the width W on the finish rolling output side is highly likely to be smaller than the target width W t small. In this case, according to the operation conditions of the hot rolling line 1 set at the current moment, it is predicted that the width W on the finish rolling output side is highly likely to be insufficient in width. Therefore, in the present embodiment, one or more operation parameters selected from the operation parameters of the finish rolling mill 6 are reset in such a way that the probability that the width W on the finish rolling output side is lower than the target width W t becomes smaller. Specifically, so that Figure 11Modify the operating parameters of the finishing mill 6 in such a way that the probability density distribution g(W) represented by a solid line changes to the probability density distribution represented by a dashed line. In this case, a prediction step of predicting statistical information on the width W of the finishing output side is performed before loading the rough rolled piece into the finishing mill 6, whereby the computer 91 is controlled to re-execute the setting calculation using the modified operating parameters of the finishing mill 6. Thus, the operating parameters of the finishing mill 6 are set in such a way that the probability of the width W of the finishing output side being lower than the target width W t becomes smaller. The re-set operating parameters are preferably selected from the operating parameters used in the input of the width prediction model M. In Figure 11 , the re-set operating parameters of the finishing mill 6 are again set as the input of the width prediction model M and the statistical information on the width W of the finishing output side is output. As shown by the dashed line in Figure 11 , confirm whether the probability of the width W of the finishing output side being lower than the target width W t becomes smaller, whereby it is possible to determine whether appropriate operating conditions have been re-set.

[0126] On the other hand, as shown in Figure 12 , it is also possible to predict that the probability of the width W of the finishing output side being lower than the target width W compared to the probability density distribution g(W) of the width of the finishing output side predicted by the width prediction model M t is high. In this case, the control target value W of the finishing width control is set in such a way that the probability of the width W of the finishing output side being lower than the target width W t becomes smaller. Thus, using the set control target value W c to perform the finishing width control of the hot rolling line 1, even if the width W of the finishing output side fluctuates, it is possible to reduce the probability of width shortage relative to the target width W c . Moreover, it is preferable to re-set one or more operating parameters selected from the operating parameters of the finishing mill 6 in such a way that the target width W t satisfies the following mathematical formula (1). t

[0127] [Equation 19]

[0128] W m – 2.5W σ ≦ W t ≦ W m -1.5W σ …(1)

[0129] Figure 13 is a schematic diagram showing the relationship between the probability density distribution g(W) of the width W of the finishing output side predicted by the width prediction model M and the target width W t . In the above mathematical formula (1), it means that the target width W t ​at the average width W of the finish-rolled output-side width W output from the width prediction model M m and the standard deviation W σ and determining W m -2.5W σ and W m -1.5W σ within the range. In this case, the target width W t can be made constant and one or more operation parameters selected from the operation parameters of the finishing mill 6 can be reset in such a way that the probability density distribution g(W) of the finish-rolled output-side width W output from the width prediction model M satisfies the above mathematical formula (1). Figure 14 is a graph showing the relationship between the deviation of the finish-rolled output-side width W from the target width W t and the amount of trimming of the steel plate. As can be seen from Figure 14 , regardless of whether the finish-rolled output-side width W is too large or too small with respect to the target width Wt, the amount of trimming of the steel plate increases and the product yield of the hot-rolled steel plate decreases. Specifically, when the finish-rolled output-side width W is too large with respect to the target width W t , trimming is required in subsequent processes in order for the hot-rolled steel plate to meet the width specification. On the other hand, when the finish-rolled output-side width W is too small with respect to the target width W t , it is impossible to form a steel plate product and a part needs to be scrapped. However, compared with the case where the finish-rolled output-side width W is too small with respect to the target width W t , the case where the finish-rolled output-side width W is too large with respect to the target width W t suppresses the amount of trimming of the steel plate. Therefore, the above mathematical formula (1) is a mathematical formula for setting the operation parameters of the finishing mill 6 in such a way that even if fluctuations in the finish-rolled output-side width W occur with respect to the target width W t , the probability of the finish-rolled output-side width W being too small becomes low. That is, the lower limit value of the mathematical formula (1) relative to the target width W t is used to reduce the probability of the finish-rolled output-side width W being too small, and the upper limit value relative to the target width W t is used to prevent the finish-rolled output-side width W from becoming too large with respect to the target width W t .

[0130] In the width control method of the finish-rolled product in this embodiment, not only corresponding to the classification of the steel grade and size of the slab, the product dimensions of the hot-rolled steel sheet, etc., but also corresponding to different operating conditions for each hot-rolled steel sheet to output the statistical information of the width on the finish-rolled output side, so that the fluctuation of the width on the finish-rolled output side of each hot-rolled steel sheet can be predicted. Thus, it is not necessary to preset the excess width in accordance with the classification of the steel grade and size of the steel sheet as in the prior art, and an appropriate excess width can be given to each hot-rolled steel sheet manufactured on the hot-rolling line, improving the product yield of the hot-rolled steel sheet. Moreover, the width control method of the finish-rolled product in this embodiment can also perform a prediction step of predicting the statistical information of the width on the finish-rolled output side at any time during the period from when the front end portion of the rough-rolled product is loaded into the finishing mill 6 to when the tail end portion passes through the finishing mill 6. Thus, the so-called dynamic finish-rolled width control can be achieved. Specifically, during finish rolling, the actual value of the operating parameters of the finishing mill 6 at the current moment can be obtained, and the width on the finish-rolled output side when the steel sheet to be loaded into the rolling stand F1 of the finishing mill 6 is discharged from the rolling stand F7 can be predicted. And at any time, the statistical information of the width on the finish-rolled output side is predicted, and based on the predicted statistical information, one or more operating parameters selected from the operating parameters of the finishing mill 6 are set in such a way that the probability of the width W on the finish-rolled output side being lower than the target width W t becomes smaller. Thus, even when a width defect occurs locally at the front end portion of the hot-rolled steel sheet, width defects can be prevented in other regions, and a decrease in the product yield can be suppressed. In this case, as the width data of the rough-rolled product, it is preferable to use the measured value of the width of the rough-rolled product measured at each position in the length direction of the rough-rolled product. This is because thereby the width prediction accuracy at each position in the length direction of the hot-rolled steel sheet is improved, and the control accuracy of the width of the hot-rolled steel sheet is also improved.

[0131] Example

[0132] 〔Example 1〕

[0133] In this embodiment, the width prediction method and width control method of the steel plate of the present invention are applied to the hot rolling line 1. The hot rolling line 1 includes a width adjusting stamping device 4 arranged on the downstream side of the heating furnace 2, a roughing mill 5 composed of four reversible rolling mills and one non-reversible rolling mill, and a finishing mill 6 composed of seven rolling mill stands. In this embodiment, on the above-mentioned hot rolling line 1, a slab with a slab thickness of 250-270 mm and a slab width of 600-1600 mm is heated by the heating furnace 2 to manufacture a hot rolled steel plate with a plate thickness of 30-35 mm on the output side of the roughing mill 5 and a plate thickness of 2-3 mm on the output side of the finishing mill 6. Moreover, the hot rolling line 1 is equipped with a roughing output side width gauge 11, a finishing output side width gauge 12, and a width gauge 13 in front of the coiler. Also, the control computer 91 and the host computer 92 of the hot rolling line 1 collect the set values and measured values of the width on the roughing output side and the set values and actual performance values of the operating parameters of the finishing mill 6, and obtain these actual performance data through the data acquisition unit 103. As the measured value of the width of the roughing piece and the actual performance data of the finishing mill 6, the data acquisition unit 103 obtains the set values of the input side plate thickness, reduction, workpiece roll circumferential speed, workpiece roll diameter, and the actual performance values of the temperatures of the front end and the tail end of the steel plate measured on the input side of the finishing mill 6 in all the rolling mill stands. On the other hand, the data acquisition unit 103 calculates the average width of the stable part of the steel plate based on the actual performance value of the finishing output side width gauge 12 and sets it as the actual performance data of the finishing output side width. Regarding the actual performance data of the finishing output side width, through the data acquisition unit 103, it is associated with the above-mentioned actual performance data of the operation, thereby generating a data set for one finishing piece and storing it in the database unit 101. Then, at the stage when 30,000 data sets are stored in the database unit 101, these data sets are divided into 20,000 learning data and 10,000 test data, and the learning data is used and the width prediction model M is generated by the machine learning unit 102. In this embodiment, as the kernel function of the Gaussian process regression, the radial basis function (RBF) kernel is used. Also, as the Gaussian noise, noise with a constant variance σ that does not depend on the learning data is used. e 2 The kernel function used in this embodiment is represented by the following mathematical formula (19). Among them, ||x (i) -x (j) || represents the Euclidean distance between the output vectors.

[0134] [Equation 20]

[0135] k(x (i) ,x (j) ) = exp(-||x (i) -x (j) || 2 / 2θ 2 )…(19)

[0136] In this embodiment, the hyperparameters of the width prediction model M are determined by using the Gaussian process regression method with learning data. Then, the operation actual data of the test data is input to the prediction unit 112 of the width prediction unit 110, and the average value W of the width on the finish rolling output side, which is the output of the width prediction model M, is obtained m and the standard deviation W σ . Then, based on the actual data W of the width W on the finish rolling output side in the test data a and the average value W of the width on the finish rolling output side m , the RMSE (root mean square error) is calculated based on the deviation therebetween. In addition, the number of test data within the range of W a ±W m and the number of test data within the range of W σ ±1.96W m are respectively obtained, and the ratio of the number of test data falling into those ranges to all the test data is calculated. As a result, the RMSE calculated based on the deviation between the actual data W of the width W on the finish rolling output side σ and the average value W of the width on the finish rolling output side is 0.1 mm, which is good. In addition, the probability that the width W on the finish rolling output side falls into the range of W a ±W m is 67.3%, and the probability that it falls into the range of W m ±1.96W σ is 95.3%. It is confirmed that in the case where the fluctuation of the width W on the finish rolling output side is assumed to follow a normal distribution, the respective probabilities are 68.3% and 95.0%. Therefore, the width prediction model M of this embodiment can accurately predict the fluctuation of the width W on the finish rolling output side. On the other hand, the width prediction model M generated as described above is stored in the prediction unit 112 of the width prediction unit 110, and width control is performed on steel plates with a slab width in the range of 1000 to 1200 mm. In this case, at the moment when the rough rolling of each rough rolling piece is completed and the measured value of the width on the rough rolling output side is obtained by the rough rolling output side width meter 11, the width prediction model M is used to calculate the statistical information of the width on the finish rolling output side, so as to target the width W of the width W on the finish rolling output side set for each steel plate m ±1.96W σ . tReset the operating parameters of the finishing mill 6 in a manner that satisfies the relationship shown in the above mathematical formula (1). As the operating parameters of the reset finishing mill 6, the inter-stand tension in the finishing mill 6 was selected. The steel plate finished rolled in this way was cooled in the discharge roller table to produce a hot-rolled steel plate. The number of the produced hot-rolled steel plates was 400 rolls. As a result, the proportion of the rolls with a width lower than the target width before the coiler was reduced by 35% in this embodiment compared with the conventional example where the excess width was preset. Moreover, the amount of the trimmed edge cut off due to the width being too large compared with the target width before the coiler was reduced by 0.8 mm on average in this embodiment. Based on the above content, it was confirmed that the statistical information of the width of the finished rolled product could be predicted through this embodiment, and the width defects of the hot-rolled steel plate could be reduced and the product yield could be improved by applying the width control to the finished rolled product.

[0137] 〔Example 2〕

[0138] As an embodiment of the present invention, another example of the width prediction method for the finished rolled product will be described. In the above Example 1, when accumulating the actual performance data in the database unit 101, the data acquisition unit 103 acquired the actual performance data related to the slab dimensions, i.e., the thickness, width, and length of the slab, as the attribute information of the slab. And the data acquisition unit 103 acquired the actual performance data related to the component composition of the slab, i.e., the respective content actual performance data of C, Si, Mn, P, S, Nb, Ti, Cu, Ni, Mo, and B in the slab, as the attribute information of the slab. Moreover, the actual performance data of these slab attribute information were accumulated in the database unit 101 as a data set corresponding to the actual performance data acquired in Example 1 in the data acquisition unit 103.

[0139] In this embodiment, also at the stage when 30,000 data sets were accumulated in the database unit 101, these data sets were divided into 20,000 learning data and 10,000 test data, and the learning data were used to generate the width prediction model M by the machine learning unit 102. When performing machine learning, the radial basis function (RBF) kernel was used as the kernel function of the Gaussian process regression.

[0140] In this embodiment, the width prediction model M generated is a width prediction model learned by the method of Gaussian process regression. This width prediction model uses, as input data, the measured value of the width of the rough-rolled piece, the operating parameters of the finishing mill, and the parameters selected from the slab attribute information, and uses the statistical information of the width of the finished-rolled piece as output data. The operating parameters of the finishing mill used in the input data are the same as those in Embodiment 1, namely, the input side plate thickness, reduction, workpiece roll circumferential speed, workpiece roll diameter, and the temperatures of the front end and the tail end of the steel plate on the input side of the finishing mill for all the rolling mill stands of the finishing mill 6. Moreover, the parameters of the slab attribute information used in the input data are the information related to the slab dimensions, i.e., the slab thickness, slab width, and slab length, and the information related to the composition of the slab, i.e., the respective contents of C, Si, Mn, P, S, Nb, Ti, Cu, Ni, Mo, and B in the slab.

[0141] In this embodiment, the hyperparameters of the width prediction model M are determined by the method of Gaussian process regression using the learning data. Moreover, the operation performance data of the test data are input to the prediction unit 112 of the width prediction unit 110, and the average value Wm and the standard deviation Wσ of the width W on the finishing output side, which are the outputs of the width prediction model, are obtained. And, the RMSE (root mean square error) is calculated based on the deviation between the actual performance data Wa of the width W on the finishing output side, which is the test data, and the average value Wm. In addition, the number of test data for which the actual performance data Wa of the width W on the finishing output side is within the range of Wm ± Wσ is respectively obtained, and the ratio of the number of test data falling into those ranges to all the test data is calculated.

[0142] As a result, based on the generated width prediction model M, the RMSE calculated from the deviation between the actual performance data Wa of the width W on the finishing output side and the average value Wm is 0.0 mm. And, the probability that the width W on the finishing output side falls within the range of Wm ± Wσ is 65.3%, which is a value close to the probability of 68.3% in the case where it is assumed that the fluctuation of the width W on the finishing output side follows a normal distribution. From the above, it can be confirmed that, according to the present invention, the statistical information of the width on the finishing output side, i.e., the average value Wm and the standard deviation Wσ of the width on the finishing output side, can be predicted with high precision.

[0143] The above has described the embodiments to which the invention completed by the present inventor is applied, but the present invention is not limited by the description and the drawings that are part of the disclosure of the present invention based on this embodiment. That is, other embodiments, examples, and application techniques and the like completed by those skilled in the art based on this embodiment are all included in the scope of the present invention.

[0144] Industrial Applicability

[0145] According to the present invention, a method for predicting the width of a finish-rolled product can be provided, which can predict statistical information including fluctuations in the width of the finish-rolled product. Further, according to the present invention, a method for controlling the width of a finish-rolled product can be provided, which can take into account fluctuations in the width of the finish-rolled product and control the width in the length direction of the finish-rolled product with high precision. Moreover, according to the present invention, a method for manufacturing a hot-rolled steel sheet can be provided, which can improve the product yield of the hot-rolled steel sheet. Additionally, according to the present invention, a method for generating a width prediction model of a finish-rolled product can be provided, which can generate a width prediction model for predicting statistical information including fluctuations in the width of the finish-rolled product.

[0146] Description of Reference Numerals

[0147] 1 Hot rolling line;

[0148] 2 Heating furnace;

[0149] 3 Descaler;

[0150] 4 Width-adjusting stamping device;

[0151] 5 Roughing mill;

[0152] 6 Finishing mill;

[0153] 7 Cooling device;

[0154] 8 Coiler (winder);

[0155] 11 Width gauge on the roughing output side;

[0156] 12 Width gauge on the finishing output side;

[0157] 13 Width gauge before the coiler (width gauge on the coiler input side);

[0158] 14 Width gauge on the finishing input side;

[0159] 15 Rolling path line;

[0160] 16a, 16b, 16c, 16d Cameras;

[0161] 61 Crop shear;

[0162] 62a, 62b Work rolls;

[0163] 63a, 63b Backup rolls;

[0164] 64a, 64b Bearing parts (backup roll supports);

[0165] 65 Housing;

[0166] 66 Load cell;

[0167] 67 Lower pressing cylinder;

[0168] 68a, 68b Bearing housings (workpiece roll supports);

[0169] 69 Looper;

[0170] 69a Looper roll;

[0171] 90 Controller for control;

[0172] 91 Computer for control;

[0173] 92 Host computer;

[0174] 100 Width prediction model generation unit;

[0175] 101 Database unit;

[0176] 102 Machine learning unit;

[0177] 103 Data acquisition unit;

[0178] 110 Width prediction unit;

[0179] 111 Input data acquisition unit;

[0180] M Width prediction model;

[0181] SA Rough rolled piece;

[0182] SB Steel plate.

Claims

1. A method for predicting the width of a finish-rolled product, which predicts the width of the finish-rolled product in a hot rolling line. The hot rolling line includes a heating furnace for heating a slab, a roughing mill for roughing the heated slab to produce a rough-rolled product, and a finishing mill for finishing the rough-rolled product to produce the finish-rolled product. The method is characterized in that the method for predicting the width of the finish-rolled product includes a prediction step of using a width prediction model learned by the method of Gaussian process regression to predict the statistical information of the width of the finish-rolled product. The width prediction model includes, as input data, the set value or measured value of the width of the rough-rolled product and one or more operation parameters selected from the operation parameters of the finishing mill, and takes the statistical information of the width of the finish-rolled product as output data.

2. The method for predicting the width of a finish-rolled product according to claim 1, wherein the width prediction model includes, as input data, one or more parameters selected from the attribute information of the slab.

3. A method for controlling the width of a finish-rolled product, wherein the method for controlling the width of the finish-rolled product includes a setting step of using the method for predicting the width of the finish-rolled product according to claim 1 or 2 to predict the statistical information of the width of the finish-rolled product, and setting one or more operation parameters selected from the operation parameters of the finishing mill in such a way that the probability that the width of the finish-rolled product is lower than the target width becomes smaller based on the predicted statistical information.

4. The method for controlling the width of a finish-rolled product according to claim 3, The statistical information on the width of the finish-rolled piece includes the average value W of the width of the finish-rolled piece m and the standard deviation W σ , and the setting step includes setting one or more operation parameters selected from the operation parameters of the finishing mill in such a way that the target width W of the finish-rolled piece t satisfies the relationship shown in the following mathematical formula (1), [Equation 1] W m -2.5W σ ≤W t ≤W m -1.5W σ …(1).

5. A method for manufacturing a hot-rolled steel sheet, which includes a step of manufacturing a hot-rolled steel sheet by using the method for controlling the width of a finish-rolled product according to claim 3 or 4.

6. A method for generating a width prediction model for a finish-rolled product, which generates a width prediction model for predicting the width of the finish-rolled product in a hot rolling line. The hot rolling line includes a heating furnace for heating a slab, a roughing mill for roughing the heated slab to produce a rough-rolled product, and a finishing mill for finishing the rough-rolled product to produce the finish-rolled product. The method is characterized in that the method for generating the width prediction model for a finish-rolled product includes: a learning data acquisition step of acquiring a plurality of learning data, where the plurality of learning data includes actual performance data of the set value or measured value of the width of the rough-rolled product, one or more actual performance data selected from the actual performance data of the finishing mill, and actual performance data of the width of the finish-rolled product; a step of generating the width prediction model by using the plurality of learning data acquired in the learning data acquisition step and using the method of Gaussian process regression. The width prediction model includes, as input actual performance data, the actual performance data of the set value or measured value of the width of the rough-rolled product and one or more actual performance data selected from the actual performance data of the finishing mill, and takes the statistical information of the width of the finish-rolled product as output data.

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