JP7616438B2 - Width control method for finish rolled material and manufacturing method for hot rolled steel sheet - Google Patents

Description

The present invention relates to a method for predicting the width of finishing rolled material in a hot rolling line, a method for controlling the width of finishing rolled material, a method for manufacturing hot rolled steel plate, and a method for generating a width prediction model for finishing rolled material.

In a hot rolling line, first, a slab, which is a steel material, is heated in a heating furnace, the width of the slab is adjusted by a width reduction press (sizing press), and then one or more rough rolling mills are used to roughly roll the slab to produce a semi-finished steel plate called a rough bar with a thickness of approximately 30 to 50 mm (hereinafter referred to as rough rolled material). Next, the head and tail ends of the rough rolled material are cut off by a crop shear, and the rough rolled material is finish rolled by a finishing mill consisting of 5 to 7 rolling stands capable of continuous rolling, producing a steel plate with a thickness of approximately 1.0 to 25.0 mm (hereinafter referred to as finish rolled material). Finally, the finish rolled material, which is in a high temperature state, is cooled by a cooling device on the run-out table, and then wound by a coiler (winder) to become a hot-rolled steel plate. In a hot rolling line, the width of a steel sheet varies in a complex manner during the manufacturing process of the hot rolled steel sheet, since the steel sheet is plastically deformed in the thickness direction and width direction in the width reduction press, rough rolling mill, and finish rolling mill. On the other hand, the width accuracy of the hot rolled steel sheet has a direct effect on the product yield. For this reason, in a hot rolling line, the width of the rough rolled material is controlled (rough width control) at the stage after rough rolling and before being charged into the finish rolling mill, and the width of the steel sheet is controlled (finish width control) during the process of passing through the finish rolling mill.

In a hot rolling line, the width of a steel sheet changes due to various causes, and therefore various techniques have been proposed to improve the width accuracy of the hot rolled steel sheet. For example, Patent Document 1 describes a method for controlling the width of a finish rolled material (hereinafter referred to as the finish exit width). Specifically, the method described in Patent Document 1 calculates the width change amount of the steel sheet in the finish rolling mill, and controls the opening degree of the edger installed on the entry side of the rough rolling mill and/or the finish rolling mill based on the calculated value and the target value of the finish exit width, thereby controlling the finish exit width. Patent Document 1 also describes predicting the width change amount of the steel sheet in the finish rolling mill using a prediction formula with the parameters of the thickness of the steel sheet in each rolling stand, the reduction ratio, the tension between rolling stands, the crown ratio change, the deformation resistance and temperature of the steel sheet, and the passing time between rolling stands. Furthermore, the method described in Patent Document 1 calculates the prediction formula by dividing it into three regions: near the entrance of the roll bite, in the roll bite, and between the rolling stands.

Patent Document 2 also describes a method for controlling the finish exit width. Patent Document 2 also describes that when using a prediction formula for predicting the width change of the steel plate in the finish rolling mill, different formulas are applied as prediction formulas for the width change near the roll bite depending on whether the crown ratio change in each rolling stand is positive or negative. Patent Document 3 also describes a method for correcting the target value of the width of the steel plate based on the deviation of the actual measured value of the width of the steel plate obtained at the beginning of rolling from the target value when controlling the finish exit width. That is, the method described in Patent Document 3 obtains actual data of the width change of the steel plate during finish rolling at the beginning of rolling, and corrects the target value of the width of the steel plate based on this.

Japanese Patent Application Publication No. 5-285516 Japanese Patent Application Publication No. 8-112609 JP 2006-51512 A

"Gaussian Processes and Machine Learning", by Daichi Mochihashi and Shigeyuki Ohba, published 2019/03/07 ISBN978-4-06-152926-7, Kodansha

However, the prediction formula used in the method described in Patent Document 1 calculates a representative value of the width change of the steel plate in the finishing rolling mill, but does not predict the variation in the width change of the steel plate. Therefore, according to the method described in Patent Document 1, the width change of the steel plate varies due to factors such as an error in estimating the temperature of the steel plate during finishing rolling, and it is inevitable that the finishing exit width will be too small or too large. Similarly, the method described in Patent Document 2 calculates a representative value of the width change of the steel plate in the finishing rolling mill, but does not predict the variation in the width change of the steel plate. Therefore, it is inevitable that the finishing exit width will be too small or too large. In contrast, the method described in Patent Document 3 attempts to identify the variation in the width change of the steel plate in the finishing rolling mill based on actual measurement data obtained at the beginning of rolling. However, since the width change of the steel plate in the finishing rolling mill varies due to changes in operating conditions, there is room for improvement in terms of predicting the variation in the width change of the steel plate with high accuracy.

As described above, conventional finishing width control attempts to improve the precision of the finishing delivery width by predicting the width change of the steel plate using a strict physical model or by identifying the variability in the width change of the steel plate obtained from actual values. However, it is inevitable that the width change of the steel plate in the finishing rolling mill will vary due to various causes. For this reason, the width of the steel plate may be too small or too large, which inevitably leads to poor width precision of the hot-rolled steel plate and reduced product yield.

The present invention has been made to solve the above problems, and an object of the present invention is to provide a width prediction method for finish rolled material capable of predicting statistical information including the width variation of the finish rolled material. Another object of the present invention is to provide a width control method for finish rolled material capable of accurately controlling the longitudinal width of the finish rolled material taking into account the width variation of the finish rolled material. Another object of the present invention is to provide a manufacturing method for hot rolled steel sheet capable of improving the product yield of the hot rolled steel sheet. Another object of the present invention is to provide a method for generating a width prediction model for finish rolled material capable of generating a width prediction model that predicts statistical information including the width variation of the finish rolled material.

The method for predicting the width of a finishing rolled material according to the present invention is a method for predicting the width of a finishing rolled material in a hot rolling line including a heating furnace for heating a slab, a rough rolling mill for rough rolling the heated slab to produce a rough rolled material, and a finishing rolling mill for finish rolling the rough rolled material to produce a finishing rolled material, and includes a prediction step of predicting statistical information of the width of the finishing rolled material using a width prediction model learned by a Gaussian process regression technique, which includes as input data a set value or an actual measured value of the width of the rough rolled material and one or more operating parameters selected from the operating parameters of the finishing rolling mill, and which outputs statistical information of the width of the finishing rolled material.

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

The width control method for finishing rolled material according to the present invention includes a setting step of predicting statistical information of the width of the finishing rolled material using the width prediction method for finishing rolled material according to the present invention, and setting one or more operating parameters selected from the operating parameters of the finishing rolling mill based on the predicted statistical information so as to reduce the probability that the width of the finishing rolled material falls below the target width.

The statistical information on the width of the finish rolled material includes an average value _Wm and a standard deviation _Wσ of the width of the finish rolled material, and the setting step preferably includes a step of setting one or more operational parameters selected from the operational parameters of the finish rolling mill so that the target width _Wt of the finish rolled material satisfies the relationship shown in the following mathematical formula (1).

The method for manufacturing hot-rolled steel sheet according to the present invention includes a step of manufacturing hot-rolled steel sheet using the width control method for finish rolled material according to the present invention.

The method for generating a width prediction model of a finishing rolled material according to the present invention is a method for generating a width prediction model for predicting the width of the finishing rolled material in a hot rolling line including a heating furnace for heating a slab, a rough rolling mill for rough rolling the heated slab to produce a rough rolled material, and a finishing rolling mill for finish rolling the rough rolled material to produce a finish rolled material, and includes a learning data acquisition step for acquiring multiple learning data including actual data of a set value or actual measurement value of the width of the rough rolled material, one or more operational actual data selected from the operational actual data of the finishing rolling mill, and actual data of the width of the finishing rolled material, and a step for generating the width prediction model using a Gaussian process regression technique using the multiple learning data acquired in the learning data acquisition step, the input actual data including actual data of the set value or actual measurement value of the width of the rough rolled material and one or more operational actual data selected from the operational actual data of the finishing rolling mill, and the output data including statistical information on the width of the finishing rolled material.

According to the method for predicting the width of finish rolled material of the present invention, it is possible to predict statistical information including the variation in the width of the finish rolled material. Furthermore, according to the method for controlling the width of finish rolled material of the present invention, it is possible to accurately control the longitudinal width of the finish rolled material taking into account the variation in the width of the finish rolled material. Furthermore, according to the manufacturing method of hot rolled steel sheet of the present invention, it is possible to improve the product yield of hot rolled steel sheet. Furthermore, according to the method for generating a width prediction model of finish rolled material of the present invention, it is possible to generate a width prediction model that predicts statistical information including the variation in the width of the finish rolled material.

FIG. 1 is a schematic diagram showing an example of the configuration of a hot rolling line to which the present invention is applied. FIG. 2 is a schematic diagram showing an example of the configuration of the finishing rolling mill shown in FIG. FIG. 3 is a schematic diagram showing an example of the configuration of one rolling stand that constitutes the finishing mill shown in FIG. FIG. 4 is a schematic diagram for explaining the operation of a looper disposed between the rolling stands of the finishing rolling mill shown in FIG. FIG. 5 is a schematic diagram for explaining an optical width measuring method. FIG. 6 is a flowchart showing the flow of the model generation steps according to one embodiment of the present invention. FIG. 7 is a flowchart showing the flow of the prediction step according to one embodiment of the present invention. FIG. 8 is a block diagram showing the configuration of a width prediction model generating unit according to an embodiment of the present invention. FIG. 9 is a diagram for explaining a method of setting a control target width in a conventional width control method. FIG. 10 is a block diagram showing the configuration of a width prediction unit according to an embodiment of the present invention. FIG. 11 is a diagram showing the relationship between the probability density distribution of the finish delivery width predicted by the width prediction model and the target width. FIG. 12 is a diagram for explaining a method for setting a control target value for finishing width control in this embodiment. FIG. 13 is a diagram showing the relationship between the probability density distribution of the finish delivery width predicted by the width prediction model and the target width. FIG. 14 is a diagram showing the relationship between the deviation of the finish delivery width from the target width and the amount of cut-off of the steel plate.

Below, with reference to the drawings, a method for predicting the width of finishing rolled material, a method for controlling the width of finishing rolled material, a method for manufacturing hot-rolled steel sheet, and a method for generating a width prediction model for finishing rolled material, which are one embodiment of the present invention, are described in detail.

[Hot rolling line]
First, the configuration of a hot rolling line to which the present invention is applied will be described with reference to Figs.

Figure 1 is a schematic diagram showing an example of the configuration of a hot rolling line to which the present invention is applied. As shown in Figure 1, the hot rolling line 1 to which the present invention is applied is equipped with a heating furnace 2, a descaling device 3, a width reduction press device 4, a rough rolling mill 5, a finishing rolling mill 6, a cooling device 7, and a coiler (winder) 8. A cast slab (not shown) is charged into the heating furnace 2, heated to a predetermined set temperature, and extracted from the heating furnace 2 as a hot slab. The hot slab extracted from the heating furnace 2 has the primary scale formed on its surface removed by the descaling device 3, and then is width-reduced to a predetermined set width by the width reduction press device 4. The width-reduced slab is rolled to a predetermined thickness in the rough rolling mill 5 to become a rough rolled material, and is transported to the finishing rolling mill 6. In the finishing rolling mill 6, the rough rolled material is rolled to a product thickness by a continuous rolling mill consisting of 5 to 7 rolling stands to become a finish rolled material. Downstream of the finishing mill 6, a cooling device 7 is provided in a facility called a run-out table, and the finish-rolled material is cooled to a predetermined temperature and then wound into a coil by a coiler 8.

In addition, multiple width gauges are installed as width measuring means in the middle of the conveying process of the hot rolling line 1. In the example shown in FIG. 1, a rough exit width gauge 11 is installed at the exit side of the rough rolling mill 5, and a finish exit width gauge 12 is installed at the exit side of the finish rolling mill 6. In addition, a pre-coiler width gauge (coiler entry width gauge) 13 is installed at the exit side of the cooling device 7 to measure the width of the finish rolled material before coiling. In addition, a finish entry width gauge 14 is installed at the entry side of the finish rolling mill 6 to measure the width of the rough rolled material. However, if there is no means for imparting plastic deformation to the rough rolled material between the rough rolling mill 5 and the finish rolling mill 6, the width of the rough rolled material measured by the rough exit width gauge 11 and the width of the rough rolled material measured by the finish entry width gauge 14 will be the same. In this embodiment, the width of the rough rolled material measured by the rough exit width meter 11 may be referred to as the rough exit width, the width of the finish rolled material measured by the finish exit width meter 12 as the finish exit width, and the width of the steel plate measured by the pre-coiler width meter 13 as the pre-coiler width. The width of the rough rolled material measured by the finish entry width meter 14 may be referred to as the finish entry width, but this may be regarded as the same as the rough exit width.

The hot rolling line 1 is equipped with a programmable logic controller (PLC) 90 that controls each device constituting the hot rolling line 1, a control computer (process computer) 91 that gives control commands to the control controller 90, and a host computer 92 that gives manufacturing instructions to the hot rolling line 1. The width control of the steel plate in the hot rolling line 1 is performed by the control computer 91 setting the control target value of the rough exit width (rough control target width), the control target value of the finish exit width (finish control target width), and the control target value of the pre-coiler width (pre-coiler control target width) based on the host computer 92 or manufacturing instructions from the host computer 92, and setting the operating conditions of the rough rolling mill 5 and the finish rolling mill 6. Specifically, the host computer 92 or the control computer 91 sets a finishing target width (hereinafter sometimes simply referred to as a target width) which is a target width of a finish rolled material, taking into consideration the amount of width change of the steel sheet occurring between the exit side of the finishing mill 6 and the pre-coiler width measuring device 13, based on a pre-coiler target width (pre-coiler target width) determined from the product specifications of the hot-rolled steel sheet. Furthermore, the host computer 92 or the control computer 91 sets a target width (coarse target width) of a rough rolled material, taking into consideration the amount of width change of the steel sheet in the finishing mill 6, based on the set finishing target width. In this case, the target values of width control (coarse control target width, finish control target width, pre-coiler control target width) may be set by providing an extra width (margin) in advance for the rough target width, finish target width, and pre-coiler target width. Then, the host computer 92 or the control computer 91 sets the rolling conditions in each pass of the rough rolling so that the rough exit width coincides with the rough control target width. The host computer 92 or the control computer 91 also sets the rolling conditions in each rolling stand of the finish rolling so that the finish exit width coincides with the finish control target width. Furthermore, the host computer 92 or the control computer 91 may set the tension between the finish rolling mill 6 and the coiler 8 and the cooling conditions of the cooling device 7 so that the coiler pre-width coincides with the coiler pre-width. In this case, the finish rolling mill 6 may perform dynamic width control while referring to the actual measured values of the rough exit width and the finish exit width. The control controller 90 has a function of collecting information acquired from various sensors (thickness gauge, thermometer, etc.) in addition to information acquired from a width gauge installed in the hot rolling line 1 at a predetermined sampling period and outputting them to the control computer 91.

One embodiment of the present invention, a method for predicting the width of a finish rolled material, is a method for predicting the finish exit width. Another embodiment of the present invention, a method for controlling the width of a finish rolled material, is a method for controlling the width of a steel plate so that the finish exit width satisfies a predetermined relationship with the finish target width.

[Finishing rolling mill]
FIG. 2 is a schematic diagram showing a configuration example of the finishing mill 6 shown in FIG. 1. The rough rolled material is transported to the entrance of the finishing mill 6. As shown in FIG. 2, a crop shear 61 is arranged at the entrance of the finishing mill 6. The crop shear 61 is a device that cuts and removes crops (irregularly shaped parts at the leading and trailing ends of the rough rolled material) formed at the leading and trailing ends of the rough rolled material. As a result, the rough rolled material is shaped into a substantially rectangular planar shape that is easy to be smoothly bitten into the finishing mill 6. The rough rolled material SA charged into the finishing mill 6 is hereinafter simply referred to as a steel plate SB. The finishing mill 6 shown in FIG. 2 is composed of seven rolling stands F1 to F7, but the number of rolling stands is not limited to this. Generally, the number of rolling stands of the finishing mill 6 is 6 to 7, and it may be composed of five rolling stands. The finishing mill 6 takes the form of a hot tandem finishing mill that simultaneously rolls the steel plate SB, whose temperature has been lowered to a temperature within the range of 800 to 1100°C that is set according to the steel type, etc., in multiple rolling stands, but is simply referred to as a "finishing mill" for short.

Figures 3(a) and (b) are schematic diagrams showing an example of the configuration of one rolling stand constituting the finishing rolling mill 6 shown in Figure 2. As shown in Figures 3(a) and (b), the rolling stand has a structure with a pair of work rolls 62a, 62b on the top and bottom, sandwiching the pass line of the steel sheet SB. The work rolls 62a, 62b are supported by backup rolls 63a, 63b, respectively. The rolling load applied to the steel sheet SB is transmitted to the housing 65 via the bearing parts (backup roll chocks) 64a, 64b of the backup rolls 63a, 63b. A load cell 66, which is a load detector, is arranged between the housing 65 and the backup roll chock 64b, and the rolling load applied to the steel sheet SB can be measured by the load cell 66. In addition, the upper backup roll chock 64a and the housing 65 are connected via a compression cylinder 67, and the compression cylinder 67 can adjust the opening (roll gap) between the pair of work rolls 62a, 62b by adjusting the vertical position of the pair of work rolls 62a, 62b.

The rolling stands F1 to F7 constituting the finishing rolling 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, 62b. A typical example of a shape control actuator is a work roll bender. The work roll bender is equipped with a hydraulic device (not shown) that applies force between the bearing boxes (work roll chocks) 68a, 68b at both ends of the pair of work rolls 62a, 62b. The hydraulic device applies a bending force to the pair of work rolls 62a, 62b by applying a force between the upper and lower work roll chocks 68a, 68b, and adjusts the roll gap distribution by applying a deflection deformation to the pair of work rolls 62a, 62b. At this time, the force applied between the upper and lower work roll chocks 68a, 68b is called the bender force. In addition to the work roll bender, the rolling stands F1 to F7 are often equipped with other shape control actuators as shape control actuators. For example, in the case of a pair cross mill, the upper work roll 62a and the upper backup roll 63a are set as a pair, and are inclined (crossed) in a horizontal plane relative to the lower work roll 62b and the lower backup roll 63b to adjust the roll gap distribution. In this case, the angle formed by the upper and lower rolls is called the cross angle, and the roll gap distribution changes by changing the cross angle. In addition, the shape control actuator may use a work roll shift in which a pair of work rolls 62a, 62b are shifted in opposite directions to each other with respect to the axial direction. Furthermore, in the case of a rolling mill with a six-high rolling stand, an intermediate roll shift is used in which the upper and lower intermediate rolls are shifted in opposite directions to each other with respect to the axial direction of the rolls. The shape control actuator provided in the rolling stand can adjust the width of the steel sheet SB by changing the crown ratio of the steel sheet SB by adjusting the distribution of the roll gap.

Figure 4 is a schematic diagram for explaining the operation of the looper arranged between the rolling stands F1 to F7 of the finishing rolling mill 6 shown in Figure 2. The looper 69 shown in Figure 4 is a device for adjusting the balance between the conveying speed of the steel sheet SB discharged from the rolling stand Fi on the upstream side and the conveying speed of the steel sheet SB charged into the rolling stand Fi+1 on the downstream side. The looper 69 is equipped with a looper roll 69a whose tip contacts the steel sheet SB. The looper 69 controls the looper angle Lθ and the looper height LH so that the inter-rolling stand tension applied to the steel sheet SB between the rolling stand Fi and the rolling stand Fi+1 is within a predetermined range. Also, the work roll peripheral speed of the upstream rolling stand Fi is controlled so that the looper height LH is within a predetermined range. In this case, the inter-rolling stand tension may be measured using a load detector arranged on the looper roll 69a. Also, the inter-rolling stand tension may be estimated from the torque loaded on the electric motor for driving the looper 69. In any case, since the width of the steel sheet SB changes depending on the tension between the rolling stands, the tension between the rolling stands applied to the steel sheet SB is measured between the rolling stands of the finishing mill 6.

[Width meter]
Return to FIG. 1. The width of the steel sheet in the hot rolling line 1 is measured by a rough-exit side width gauge 11, a finish-exit side width gauge 12, a coiler pre-width gauge 13, and a finish-entry side width gauge 14. An optical width measuring method is often used for these width gauges. In the optical width measuring method, a light source is arranged below the pass line along which the steel sheet is transported, and an image sensor is arranged above the pass line, and the width of the steel sheet is measured based on the shadow length in the width direction of the steel sheet of a light beam emitted from the light source while the steel sheet passes through. Some width gauges use a camera to identify the position of the width direction end of the steel sheet and measure the width. FIGS. 5(a) and (b) are schematic diagrams showing a configuration example of a rough-exit side width gauge using a camera. In the example shown in FIG. 5(a), a pair of cameras 16a and 16b provided in the rough-exit side width gauge take an image of the steel sheet SB including the width direction end of the steel sheet SB. CMOS or CCD sensors are used for the cameras 16a and 16b. Then, an image processing unit provided in the rough-out side width gauge identifies the positions of the widthwise ends of the steel sheet SB from the images captured by the cameras 16a and 16b, and calculates the width W of the steel sheet SB based on the installation interval of the cameras 16a and 16b. Reference numeral 15 in the figure indicates a pass line. However, since this width gauge images the widthwise ends of the steel sheet SB from an oblique direction, a width measurement error is likely to occur when the steel sheet SB floats up from the pass line 15. Therefore, the width gauge often has a function of correcting the width measurement error in response to the floating of the steel sheet SB from the pass line. Specifically, as shown in FIG. 5(b), when the steel sheet SB is transported at a height of the floating amount H from the pass line 15, the width measurement error is corrected as follows. That is, first, a pair of cameras 16a and 16b arranged in the width direction of the steel sheet SB identifies both widthwise ends of the steel sheet SB, thereby identifying the measured width value W1. Next, another pair of cameras 16c, 16d arranged in the width direction of the steel plate SB also identify both ends of the steel plate SB in the width direction, thereby identifying a measured width value W2. Then, based on the positional relationship between the two pairs of cameras (in the example shown in FIG. 5(b), the distance D between the cameras 16a, 16b in the width direction and the distance L between the cameras 16a (16b) and 16c (16d) in the width direction), the actual width W of the steel plate SB is calculated by the following formula (2), which becomes the measured width value of the steel plate SB.

However, as another width measurement method, a method is sometimes used in which a laser beam is emitted in the width direction of the steel plate, the reflected light from the end faces of the steel plate is received, and the width of the steel plate is measured based on the distance to both end faces of the steel plate. Some width gauges are equipped with a thermal expansion correction function that converts the width of the steel plate after cooling based on the temperature of the steel plate. Since the width of the steel plate is measured using a width gauge during the steel plate transportation process, the width measurement value of the steel plate obtained by the width gauge becomes time-series numerical information corresponding to the sampling pitch of the width gauge. In addition, using information on the transportation speed at which the steel plate passes the position of the width gauge, it is converted into the relationship between the longitudinal position of the steel plate and the actual value of the width of the steel plate. Then, in the control computer 91, a representative value of the width of the steel plate is calculated based on the acquired actual width measurement value of the steel plate. The representative value of the width of a steel plate may be, for example, the average value of the width of the steel plate in the longitudinal direction of the steel plate (average width), the actual measured value of the width of the steel plate in the steady portion excluding the leading and trailing ends of the steel plate (steady width), the actual measured value of the width of the steel plate at the leading end of the steel plate (leading end width), or the actual measured value of the width of the steel plate at the trailing end of the steel plate (tailing end width). In addition, the minimum value (minimum width) or maximum value (maximum width) of the width of the steel plate in the longitudinal direction of the steel plate may be calculated. The actual measured value of the width of the steel plate measured by a width gauge may be expressed as a deviation from a preset target width.

[Gaussian process regression]
The finish rolled material width prediction method according to one embodiment of the present invention predicts the finish exit width in the hot rolling line 1. The finish rolled material width prediction method according to one embodiment of the present invention uses a width prediction model trained by a Gaussian process regression technique, which includes a set value or an actual measurement value of the rough rolled material width and one or more operation parameters selected from the operation parameters of the finishing rolling mill 6 as input data, and uses statistical information on the finish exit width as output data. The Gaussian process regression technique applied to the finish rolled material width prediction method according to one embodiment of the present invention will be described below.

Gaussian process regression, also called Gaussian process regression or Gaussian process, is a type of nonlinear regression model that estimates a function from an input variable to an output variable. The output is a probability distribution, and the use of a Gaussian distribution specified by two parameters, the mean and the variance, is called a Gaussian process, and the probability distribution can be obtained using a Bayesian estimation technique to represent the reliability and uncertainty of the estimation. For example, when m variables are selected as inputs to a width prediction model, the input variables are represented by an input vector ^x . Also, the output variable associated with the input vector x as learning data is represented by y. Hereinafter, a method of obtaining statistical information y* of the finishing exit width for a new input vector x ^* by the Gaussian process regression technique using n pieces of learning data x ^{(1) to x(n)} , y ⁽¹⁾ to ^{y (n)} will be specifically described. Since the m variables constituting the input vector x each represent a different physical quantity, the m variables may be standardized (normalized) in advance. Specifically, for each of the m variables, the mean value and standard deviation may be calculated from the n pieces of learning data, and each variable may be standardized using the calculated mean value and standard deviation. This is because standardizing the m variables in advance makes learning of hyperparameters, which will be described later, more efficient. In this case, to convert the m variables into physical quantities, it is sufficient to perform an inverse conversion using the calculated mean value and standard deviation.

In Gaussian process regression, a probability model is used in which a function f(x) representing an output variable y is estimated from an input variable x, and Gaussian noise is added to this. For example, the probability model is expressed as the following formula ( ³ ). In this case, it is assumed that the function f(x) follows a multivariate Gaussian distribution. It is also assumed that the Gaussian noise ε ⁽ⁱ⁾ follows a Gaussian distribution with a mean of zero and a variance of _σe (i)2. However, the Gaussian noise ε ⁽ⁱ⁾ may be a value that depends on the n pieces of training data x ⁽¹⁾ to x ⁽ⁿ⁾ , or may be a constant noise that does not depend on the n pieces of training data x ⁽¹⁾ to x ⁽ⁿ⁾ .

The Gaussian distribution refers to a distribution whose probability density N is expressed by the following formula (4). In formula (4), μ indicates the mean value, and σ indicates the standard deviation ( ^σ2 is the variance). In other words, the Gaussian distribution is a probability density specified by the mean value μ and the standard deviation σ or variance ^σ2 . Gaussian process regression uses a multivariate normal distribution, which is a multidimensional extension of such a Gaussian distribution.

In Gaussian process regression, the mean function (mean vector) representing the multivariate Gaussian distribution is a constant (for example, zero), and the covariance matrix is expressed by a kernel function. The kernel function is a function for calculating the similarity of data. The kernel function is expressed as k(x( ⁱ⁾ , x ^(j) ) using input vectors x( ⁱ⁾ and x ^(j ) as arguments, and outputs the similarity between input vectors x ⁽ⁱ⁾ and x ^(j) . Known kernel functions such as a white kernel, a linear kernel, a polynomial kernel, a Gaussian kernel, and a Mater kernel can be used as the kernel function. Some examples of kernel functions are expressed as shown in the following formulas (5) to (7) using a parameter θ. Formula (5) shows a linear kernel, formula (6) shows a quadratic polynomial kernel, and formula (7) shows a Gaussian kernel.

Based on the above assumptions, the function f(x) that represents the output variable y from the input variable x is expressed as the following equation (8) using the probability density N.

In this case, when the Gaussian noise is a constant value σ _e ² regardless of the learning data, if the covariance matrix K _n specified by the kernel function and the covariance matrix Σ _n including the Gaussian noise are defined by the following formulas (9) and (10), formula (8) can be expressed as the following formula (11) or formula (12), where I represents a unit matrix.

The covariance matrices K _n , Σ _n included in the right-hand sides of the formulas (11) and (12) include the learning data x ⁽¹⁾ to x ⁽ⁿ⁾ that are input, and the left-hand sides of the formulas (11) and (12) include the learning data y ⁽¹⁾ to y ⁽ⁿ⁾ that are output. Therefore, the hyperparameters (parameter θ and Gaussian noise σ _e ² ) included in the kernel function may be determined so that the relationship shown in the formula (11) or the formula (12) holds. As a method for determining the hyperparameters, a method selected from among known methods may be used. For example, the hyperparameters may be calculated by calculating the likelihood function of the learning data and maximizing the log-likelihood represented by the logarithm of the calculated likelihood function. In this case, the calculation method for maximizing the log-likelihood may be an optimization method such as the Monte Carlo method or the conjugate gradient method. In addition, a method such as a cross-validation method or a marginal likelihood maximization method may be used.

Next, a method for estimating statistical information y ^* of the finishing output width for a new input vector x ^* using a function f(x) for which the hyperparameters of the kernel function have been determined will be described. An estimated value for an unknown input vector x ^* that is not included in the learning data can be expressed as in the following formula (13) by applying Bayesian estimation. In this case, a vector of a newly specified kernel function k ^* is defined as in the following formula (14).

As a result, formula (13) can be expressed as formula (15) shown below. Then, statistical information for the input vector x ^* can be calculated by formulas (16) and (17) shown below, with the mean value being _Wm and the variance being _Wσ . For details about the Gaussian process regression method, please refer to known literature (for example, Non-Patent Document 1).

In this embodiment, the step of specifying the hyperparameters so as to express the relationship of the above formula (11) or formula (12) is called the model generation step. Specifically, in the model generation step, as shown in FIG. 6, first, n pieces of learning data x ⁽¹⁾ to x ⁽ⁿ⁾ , y ⁽¹⁾ to y ⁽ⁿ⁾ are acquired from a data set stored in a database or the like (step S1). Next, a kernel function to be used for machine learning is selected from, for example, formulas (5) to (7) (step S2). Next, a Gaussian distribution with a mean value of zero and a variance of σ _e ² is set as the Gaussian noise ε(i) (step S3). Next, the covariance matrices K _n and Σ _n specified by the kernel function are calculated using formulas (9) and (10) (step S4). Then, using formulas (11) and (12) that express the relationship between the input and output of the learning data, the parameter θ and the Gaussian noise σ _e are determined as hyperparameters by a learning method using a likelihood function (step S5). A kernel function that expresses the input/output relationship of the learning data is specified by the hyperparameters determined in this way. The determined hyperparameters may be stored in a storage device of the computer that executes the model generation step. Meanwhile, the step of calculating the average value W _m and the standard deviation W _σ as statistical information for the input vector x ^* using the hyperparameters determined by the model generation step is called the prediction step. Specifically, in the prediction step, as shown in FIG. 7, first, a new input vector x ^* is acquired (step S11). Next, the hyperparameters stored in the storage device of the computer that executes the model generation step are acquired, and the kernel function k ^* for the new input vector x ^* is specified using the formula (14) (step S12). Then, using the relationships shown in the formulas (16) and (17), the predicted value for the input vector x ^* is calculated as the average value W _m and the standard deviation W _σ (step S13).

[Method of generating width prediction model]
Next, an embodiment in which the above-mentioned Gaussian process regression technique is applied as a method for generating a finish rolled material width prediction model according to one embodiment of the present invention will be described.

Figure 8 is a block diagram showing the configuration of a width prediction model generation unit according to one embodiment of the present invention. As shown in Figure 8, the width prediction model generation unit 100 of this 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 rough exit side width, one or more operation performance data selected from the operation performance data of the finishing rolling mill 6, and actual data of the finish exit side width. The database unit 101 may store one or more performance data selected from the performance data of the slab attribute information as necessary. The specific performance data stored in the database unit 101 will be described later.

The performance data stored in the database unit 101 can be appropriately acquired from the control controller 90, the control computer 91, or the host computer 92. In addition, a data acquisition unit 103 may be provided to collect these performance data, and the performance data may be temporarily stored in the data acquisition unit 103, and a data set in which multiple types of performance data are associated may be generated and then accumulated in the database unit 101. Since the data stored in the database unit 101 may be acquired at different times, it is easy to configure a data set in which the data sets correspond to each other by associating multiple types of performance data in the data acquisition unit 103. For the data set stored in the database unit 101, at least one performance data is acquired for one steel plate manufactured from one slab. For example, when the average width of the finish rolled material is used as the performance data of the finish delivery width, the representative value of the operation performance data of the finishing rolling mill 6 may be used as the performance data. In this case, the width data of the finish rolled material may be a representative value for the finish rolled material, but the set value or actual value of the width at multiple positions along the longitudinal direction of the finish rolled material may be used. Regarding the performance data of the attribute information of the slab, a representative value for one steel plate may be used as the performance data.

On the other hand, the data acquisition unit 103 may generate multiple data sets for one steel plate manufactured from one slab, and store them in the database unit 101. For example, when acquiring performance data on the width of three locations, the front end, steady state, and tail end of the finishing rolled material, as performance data on the finishing exit width, the operation performance data of the finishing rolling mill 6 acquired at the front end, steady state, and tail end of the finishing rolled material may be associated with the performance data of the finishing exit width at the corresponding positions. However, for performance data that is specified regardless of the longitudinal position of the steel plate, such as performance data of the attribute information of the slab, the performance data of the same attribute information is associated with the performance data of the finishing exit width at the front end, steady state, and tail end of the steel plate.

Furthermore, the data acquisition unit 103 may acquire actual data on the finish exit width for each position divided in the longitudinal direction for one steel plate, and the operational performance data acquired for each position in the longitudinal direction of the steel plate may be associated with the actual data on the finish exit width measured at each position and stored in the database unit 101. That is, the number of divisions in the longitudinal direction of the steel plate is set to, for example, about 20 to 200, and the actual data on the finish exit width in each division section is associated with the operational performance data corresponding to each position. In this case, although the length of the steel plate SB finish-rolled by the finishing rolling mill 6 changes for each rough rolling pass, if operational performance data at positions corresponding to the divisions in the longitudinal direction of the steel plate SB is acquired, a data set corresponding to each division section can be configured in the data acquisition unit 103. When a data set corresponding to multiple positions divided in the longitudinal direction of the steel plate is accumulated in the database unit 101, the machine learning unit 102 can also generate a different width prediction model for each position in the longitudinal direction of the steel plate.

The width prediction model generating unit 100 can be provided in a control computer 91 for controlling the production of steel sheets by the hot rolling line 1. The width prediction model generating unit 100 may be provided in a host computer 92 that gives production instructions to the control computer 91, or in an independent computer that can communicate with other devices. The machine learning unit 102 may be configured in a device separate from the database unit 101 using a device that can receive the data set stored in the database unit 101. The database unit 101 stores 100 or more data sets. Preferably, 10,000 or more data sets, more preferably 100,000 or more data sets, are stored in the database unit 101. Screening may be performed on the data stored in the database unit 101 as necessary.

The machine learning unit 102 uses the data set stored in the database unit 101 to generate a width prediction model M by machine learning using the Gaussian process regression technique. The learning data used by the machine learning unit 102 are a plurality of data sets including actual data of the set value or actual value of the rough exit side width stored in the database unit 101, one or more operation actual data selected from the operation actual data of the finishing rolling mill 6, and actual data of the finishing exit side width. The machine learning unit 102 uses the learning data to perform machine learning using the Gaussian process regression technique, which includes actual data of the set value or actual value of the rough exit side width and one or more operation actual data selected from the operation actual data of the finishing rolling mill 6 as input actual data, and uses statistical information of the finishing exit side width as output data, to generate a width prediction model M. In addition, the machine learning unit 102 may use the data set stored in the database unit 101 to perform machine learning using the Gaussian process regression technique using actual data of the attribute information of the slab SA as input actual data, to generate a width prediction model M.

In this case, machine learning refers to identifying hyperparameters to be applied to Gaussian process regression by the steps shown in FIG. 6. The width prediction model M refers to the hyperparameters identified in this manner. By identifying the hyperparameters, the input/output relationship of the learning data is identified, and it becomes possible to predict statistical information on the finishing exit width for an unknown input. In this embodiment, the statistical information on the finishing exit width, which is the output of the width prediction model M learned by Gaussian process regression, includes the predicted result of the average value of the width of the finishing rolled material and the standard deviation or variance, which is an index representing its variance. This makes it possible to predict the average value of the finishing exit width as well as its variance.

On the other hand, in the conventional technology, as described in, for example, Patent Documents 1 and 2, a prediction formula for predicting the width change amount of a steel sheet in finish rolling is used to predict the finish exit width and the average value or representative value of the width change amount of the steel sheet in the finish rolling mill, but information on the variation cannot be obtained. For this reason, a target value of the width of the steel sheet must be set by adding a preset extra width (margin). Specifically, in the conventional width control method, as shown in FIG. 9, an extra width (margin) _Wr is set in advance with respect to the target width _Wt , and the sum of the target width _Wt and the extra width _Wr is set as the control target width _Wc of the finish exit width. The reason for setting the extra width _Wr is to prevent the finish exit width from falling below the target width _Wt , since a certain variation occurs in the finish exit width. If the finish exit width falls below the target width _Wt , the width of the steel sheet after hot rolling may fall below the product target width, and the product cannot be obtained due to the insufficient width. Therefore, the hot-rolled steel sheet produced may be scrapped or the shipping destination of the product may be changed, resulting in a decrease in product yield and a delay in delivery. On the other hand, if the set extra width _Wr is too large, the width of the steel sheet after hot rolling becomes too large compared to the product target width, and it becomes necessary to trim the steel sheet to obtain the product, which reduces the product yield. That is, if an attempt is made to prevent the occurrence of insufficient width as a hot-rolled steel sheet, the finish exit width becomes too large, and if an attempt is made to suppress the decrease in yield due to the edge trimming, the width insufficiency is likely to occur. For this reason, in the conventional technology, actual data on the finish exit width and the width change amount in the finish rolling mill 6 are collected for each thickness and width classification of the hot-rolled steel sheet, and the extra width is set in advance according to the variation, and the factory personnel periodically monitor whether the setting of the extra width is appropriate.

In contrast, according to the present embodiment, the average value and statistical variation of the finish exit width are predicted according to the input operating conditions of the hot rolling line, so that an appropriate excess width can be set according to the operating conditions for each steel plate, rather than for each thickness or width category of the hot rolled steel plate as in the conventional technology. This makes it possible to suppress a decrease in product yield due to insufficient or excess width of the hot rolled steel plate caused by the variation in the finish exit width.

[Slab attribute information]
The attribute information of the slab that can be used as an input for the width prediction model M refers to information on the slab dimensions that affect the width change of the steel sheet in the finishing rolling mill 6 and information on the composition of the slab. The information on the slab dimensions is information on the thickness, width, length, and weight of the slab. The information on the composition of the slab is information on the content of the components contained in the slab, such as the C content, Si content, Mn content, P content, S content, Nb content, Ti content, Cu content, Ni content, Mo content, and B content of the slab. The information on the slab dimensions affects the temperature change of the steel sheet in the hot rolling line 1, and therefore affects the variation in the finish exit width. In addition, the information on the composition of the slab affects the deformation resistance of the steel sheet and the composition and thickness of the oxide film generated on the surface of the steel sheet. As a result, the friction force at the interface between the rolling roll and the steel sheet is affected, and the deformation state of the steel sheet changes, which affects the variation in the finish exit width. Furthermore, information on the component composition of the slab affects the behavior of short-term creep deformation between rolling stands of the finishing mill 6. This affects the width reduction in the finishing mill 6, and affects the finish delivery width variation.

[Width data for rough rolled material]
The width data of the rough rolled material (set value or actual measurement value of the width of the rough rolled material) used for inputting the width prediction model M is a set value or actual measurement value regarding the width of the rough rolled material charged into the finishing mill 6. The set value regarding the width of the rough rolled material may be a representative value regarding the width of the rough rolled material used in the setting calculation for the control computer 91 to set the operating conditions of the rough rolling mill 5 or the finishing rolling mill 6. In addition, when performing rough rolling, if the control computer 91 sets the target width or the control target width of the rough rolled material at the exit side of the rough rolling mill 5, these can be used as the width data of the rough rolled material. In addition, the control computer 91 performs setting calculations using the width of the rough rolled material at the entry side of the finishing rolling mill 6 before performing finish rolling, but the set value of the finish entry width used at this time may be used as the width data of the rough rolled material. On the other hand, the actual measurement value regarding the width of the rough rolled material can be the actual value of the rough exit side width measured by the rough exit side width meter 11. Also, it is possible to use the actual value of the finish entry width measured by the finish entry width meter 14. The actual width values of the rough rolled material measured by the rough exit width meter 11 and the finish entry width meter 14 are sent from the control controller 90 to the control computer 91, so these values can be obtained from the control computer 91 using the data acquisition unit 103.

[Finishing mill operating parameters]
The operation parameters of the finishing mill 6 used to input the width prediction model M refer to rolling operation conditions that affect the width of the steel sheet in any rolling stand of the finishing mill 6. As the operation parameters of the finishing mill 6, operation parameters that affect the width of the steel sheet in three regions corresponding to each rolling stand of the finishing mill 6, namely, the vicinity of the roll bite entrance, the roll bite, and between the rolling stands, may be used. Specifically, the thickness of the steel sheet in each rolling stand, the reduction ratio, the tension between rolling stands, the crown ratio change, the deformation resistance and the temperature of the steel sheet may be used. In addition, the rolling load, the roll gap and the work roll diameter of each rolling stand, which indirectly affect the thickness and temperature of the steel sheet in each rolling stand, may be used as the operation parameters. Furthermore, the set value or actual value of the shape control actuator, which indirectly affects the crown ratio change of the steel sheet in each rolling stand, may be used. For example, the setting value or actual value of an actuator for controlling the profile of a steel sheet by changing the deflection of the work rolls, such as the bender force of a work roll bender, the cross angle in a pair cross mill, the shift amount of an intermediate roll in a six-high rolling mill, etc., can be used. In addition to these, the operation parameters of the finishing rolling mill 6 may also include operation parameters related to the speed of the steel sheet, such as the rolling speed, acceleration rate, rolling time, the peripheral speed of the work rolls of each rolling stand, and the passing time between rolling stands. This is because they affect the temperature change and deformation resistance of the steel sheet, which in turn affects the width change amount of the steel sheet. In addition, they affect the short-term creep deformation of the steel sheet, which in turn affects the width shrinkage between rolling stands. Furthermore, the rolling length and usage time after rearrangement of the work rolls used in each rolling stand may also be used as the operation parameters of the finishing rolling mill 6. This is because the friction state between the work rolls and the steel sheet changes as the surface condition of the work rolls changes over time, which affects the width spread during rolling.

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

The operation of the width prediction unit 110 shown in FIG. 10 is performed before the finishing exit width of the steel plate manufactured in the hot rolling line 1 is measured by the finishing exit width meter 12. The operation of the width prediction unit 110 can be performed, for example, at the stage where the steel plate to be predicted is charged as a slab into the heating furnace 2 or at the stage where it is extracted from the heating furnace 2. At the stage where the slab is charged into the heating furnace 2, information on the slab dimensions and the component composition of the slab are specified by the upper computer 92 as attribute information of the slab. In addition, at the stage where the slab is charged into the heating furnace 2, the manufacturing specifications of the hot rolled steel plate are set in advance, and the corresponding standard operating parameters are specified. Therefore, the prediction step can be performed by inputting the actual data of the attribute information of the slab and the set values of other operating parameters specified as standard operating parameters corresponding to the manufacturing specifications. In addition, the prediction step can also be performed, for example, during the rolling pass of the rough rolled material by the rough rolling mill 5. During rough rolling, rough width control is performed in the rough rolling mill 5, and a target width and a control target width for the rough exit width are set, so these set values can be used as input for the width prediction model M.

Furthermore, the prediction step can be performed before the rough rolling is completed and the rough rolled material is loaded into the finishing mill 6. By completing the rough rolling, the actual measurement value of the width of the rough rolled material can be obtained, and these actual values can be used as input for the width prediction model M. In addition, the rough exit width is measured by the rough exit width meter 11 and the finishing entry width meter 14, and the control computer 91 performs the setting calculation for the finishing mill 6 based on the actual measurement value of the rough exit width, and the operating conditions of the finishing mill 6 are set. Therefore, the operating parameters of the finishing mill 6 set by the setting calculation can be used as input for the width prediction model M. The prediction step can be performed at any time after the leading end of the rough rolled material is loaded into the finishing mill 6 and before the tail end of the rough rolled material passes through the finishing mill 6. In this case, since the actual values of the operating parameters of the finishing mill 6 at the current time can be obtained, the operating parameters of the finishing mill at the current time can be used as input for the width prediction model M. This makes it possible to predict the finish exit width of the rough rolled material charged into the rolling stand F1 of the finishing mill 6 when it is discharged from the rolling stand F7.

The input data acquisition unit 111 of the width prediction unit 110 shown in FIG. 10 acquires the actual values or set values of the operation parameters of the hot rolling line 1 held by the control computer 91 or the upper computer 92 in the above manner. Then, 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, calculates a kernel function for the input data (new input vector) as shown in FIG. 7, and calculates statistical information on the finish exit width, which is output data. As described above, the operation of the width prediction unit 110 can be executed at any time until the tail end of the steel plate passes through the finish rolling mill 6, so that it may be executed multiple times in the process of manufacturing one steel plate. The statistical information on the finish exit width output in the above manner may be displayed on a monitor connected to the width prediction unit 110. The operation parameters of the finish rolling mill 6 can be reset based on the output display of the statistical information on the finish exit width, thereby suppressing the occurrence of width defects in the hot rolled steel plate.

[Finishing Rolled Material Width Control Method]
A finish rolled material width control method according to one embodiment of the present invention resets one or more operation parameters selected from the operation parameters of the finish rolling mill 6 based on the statistical information of the finish exit width predicted as described above, so as to reduce the probability that the finish exit width falls below the target width (target width) _Wt of the finish rolled material. In the above finish rolled material width prediction method, the statistical information of the finish exit width, which is the output of the width prediction model M, is specified as, for example, the average value _Wm and standard deviation _Wσ of the finish exit width. In this case, the finish exit width W is predicted to follow a probability density distribution g(W) shown in the following formula (18).

FIG. 11 is an example that shows a schematic diagram of a probability density distribution g(W) of the finish exit width predicted by the width prediction model M together with the target width _Wt . In FIG. 11, the finish exit width W is predicted to be smaller than the target width _Wt with a high probability because the average value _Wm of the finish exit width W predicted by the width prediction model M is smaller than the target width _Wt and the finish exit width W varies. In this case, the finish exit width W is predicted to be insufficient with a high probability from the operation conditions of the hot rolling line 1 that are currently set. Therefore, in this embodiment, one or more operation parameters selected from the operation parameters of the finishing rolling mill 6 are reset so that the probability that the finish exit width W falls below the target width _Wt is reduced. Specifically, the operation parameters of the finishing rolling mill 6 are corrected so that the probability density distribution g(W) shown by the solid line in FIG. 11 becomes the probability density distribution shown by the dashed line. In this case, the prediction step of predicting the statistical information of the finish exit width W is executed before the rough rolled material is charged into the finish rolling mill 6, so that the control computer 91 executes the setting calculation again using the corrected operation parameters of the finish rolling mill 6. As a result, the operation parameters of the finish rolling mill 6 are set so as to reduce the probability that the finish exit width W falls below the target width _Wt . The reset operation parameters are preferably selected from the operation parameters used as the input of the width prediction model M. In FIG. 11, the reset operation parameters of the finish rolling mill 6 are input again to the width prediction model M to output the statistical information of the finish exit width W, and it is possible to determine whether the proper operation conditions have been reset by checking whether the probability that the finish exit width W falls below the target width _Wt is reduced as shown by the dashed line in FIG. 11.

On the other hand, as shown in Fig. 12, when the probability density distribution g(W) of the finish exit width predicted by the width prediction model M predicts that the finish exit width W has a high probability of falling short of the target width _Wt , the control target value _Wc for the finish width control may be set so that the probability of the finish exit width W falling short of the target width _Wt is reduced. In this way, the finish width control of the hot rolling line 1 is performed using the set control target value _Wc , and the probability of the width being insufficient for the target width _Wt can be reduced even if there is variation in the finish exit width _W. Furthermore, it is preferable to reset one or more operation parameters selected from the operation parameters of the finishing rolling mill 6 so that the target width Wt satisfies the following mathematical formula (1).

FIG. 13 is a schematic diagram showing the relationship between the probability density distribution g(W) of the finish exit width W predicted by the width prediction model M and the target width _Wt . In the above formula (1), it means that the target width _Wt is in the range of _Wm -2.5Wσ and _Wm - _1.5Wσ specified by the average width _Wm and standard deviation _Wσ of the finish exit width W output from the width prediction model M. In this case, it is preferable to reset one or more operation parameters selected from the operation parameters of the finishing rolling mill 6 so that the probability density distribution g( _W ) of the finish exit width _W output from the width prediction model M satisfies the above formula (1) with the target width Wt being constant. FIG. 14 is a diagram showing the relationship between the deviation of the finish exit width W from the target width _Wt and the amount of cut-off of the steel plate. As can be seen from FIG. 14, even if the finish exit width W is too large or too small for the target width Wt, the amount of cut-off of the steel plate increases and the product yield of the hot-rolled steel plate decreases. In detail, if the finish exit width W is excessively large with respect to the target width _Wt , it is necessary to perform edge trimming in a subsequent process so that the hot-rolled steel sheet meets the width specification. On the other hand, if the finish exit width W is excessively small with respect to the target width _Wt , it is not possible to produce a steel sheet product, and it is necessary to scrap a part of the steel sheet. However, the amount of cut-off of the steel sheet is suppressed more when the finish exit width W is excessively large with respect to the target width _Wt than when it is excessively small with respect to the target width _Wt . For this reason, the above formula (1) sets the operation parameters of the finish rolling mill 6 so that the probability of the finish exit width W being excessively small is low even if the finish exit width W varies with respect to the target width Wt. That is, the lower limit value for the target width _Wt in formula (1) is intended to reduce the probability of the finish exit width W being excessively small, and the upper limit value for the target width _Wt is intended to prevent the finish exit width W from being excessively large with respect to the target width _Wt .

In the width control method of the finish rolled material in this embodiment, statistical information on the finish exit width is output in accordance with different operating conditions for each hot rolled steel plate, in addition to the classification of the steel type and size of the slab and the product dimensions of the hot rolled steel plate, so that the variation in the finish exit width for each hot rolled steel plate can be predicted. As a result, unlike the conventional technology, it is not necessary to set the extra width in advance according to the steel type and size classification of the steel plate, and an appropriate extra width can be given to each hot rolled steel plate manufactured in the hot rolling line, thereby improving the product yield of the hot rolled steel plate. Furthermore, in the width control method of the finish rolled material in this embodiment, the prediction step of predicting the statistical information on the finish exit width may be performed at any time from when the front end of the rough rolled material is charged into the finish rolling mill 6 until the tail end passes through the finish rolling mill 6. This allows so-called dynamic finish width control to be realized. Specifically, the actual values of the operational parameters of the finishing rolling mill 6 at the current time during the finish rolling can be obtained, and the finish exit width when the steel sheet charged into the rolling stand F1 of the finishing rolling mill 6 is carried out from the rolling stand F7 can be predicted. Then, statistical information on the finish exit width is predicted at any time, and one or more operational parameters selected from the operational parameters of the finishing rolling mill 6 are set at any time so that the probability that the finish exit width W falls below the target width _Wt is reduced based on the predicted statistical information. As a result, even if a width defect occurs in a part of the tip of the hot-rolled steel sheet, width defects can be prevented in other areas, and a decrease in product yield can be suppressed. In this case, it is preferable to use the actual measured value of the width of the rough rolled material measured at each position in the longitudinal direction of the rough rolled material as the width data of the rough rolled material. This is because the width prediction accuracy for each position in the longitudinal direction of the hot-rolled steel sheet is improved, and the control accuracy of the width of the hot-rolled steel sheet is also improved.

Example 1
In this embodiment, the steel plate width prediction method and the width control method of the present invention were applied to a hot rolling line 1 including a width reduction press device 4 arranged downstream of a heating furnace 2, a roughing mill 5 consisting of four reversible rolling mills and one non-reversible rolling mill, and a finishing mill 6 consisting of seven rolling stands. In this embodiment, in the above-mentioned hot rolling line 1, a slab having a slab thickness of 250 to 270 mm and a slab width of 600 to 1600 mm was heated by a heating furnace 2, and a hot rolled steel plate having a plate thickness of 30 to 35 mm on the delivery side of the roughing mill 5 and a plate thickness of 2 to 3 mm on the delivery side of the finishing mill 6 was produced. In addition, the hot rolling line 1 is equipped with a roughing delivery side width meter 11, a finishing delivery side width meter 12, and a coiler front width meter 13. In addition, the control computer 91 and the host computer 92 of the hot rolling line 1 collect the set value and the actual measurement value of the rough exit width and the set value and the actual value of the operation parameters of the finishing rolling mill 6, and the data acquisition unit 103 acquires these actual data. The data acquisition unit 103 acquires the actual measurement value of the width of the rough rolled material, and the set value of the entry thickness, the reduction amount, the work roll peripheral speed, the work roll diameter, and the actual values of the temperature of the front end and the tail end of the steel plate measured at the entry side of the finishing rolling mill 6 in all rolling stands as the operation actual data of the finishing rolling mill 6. On the other hand, the data acquisition unit 103 calculates the average width of the steady part of the steel plate from the actual value of the finish exit width meter 12, and this is used as the actual data of the finish exit width. The actual data of the finish exit width is associated with the above operation actual data by the data acquisition unit 103 to generate one data set for one finish rolled material, and is accumulated in the database unit 101. Then, at the stage where 30,000 data sets were accumulated in the database unit 101, these data sets were divided into 20,000 pieces of training data and 10,000 pieces of test data, and the width prediction model M was generated by the machine learning unit 102 using the training data. In this embodiment, a radial basis function (RBF) kernel was used as the kernel function of the Gaussian process regression. Moreover, a noise having a constant variance σ _e ² was used as the Gaussian noise, regardless of the training data. The kernel function used in this embodiment is expressed by the following formula (19). Here, ||x ⁽ⁱ⁾ - x ^(j) || represents the Euclidean distance between the input vectors.

In this embodiment, the hyperparameters of the width prediction model M were specified by a Gaussian process regression method using the learning data. Then, the operation performance data of the test data was input to the prediction section 112 of the width prediction section 110, and the average value _Wm and standard deviation _Wσ of the finish exit width, which are the output of the width prediction model M, were obtained. Then, the RMSE (root mean square error) was calculated from the deviation between the actual data _Wa of the finish exit width W, which is the test data, and the average value _Wm of the finish exit width. Furthermore, the number of test data in which the actual data _Wa of the finish exit width W falls within the range of _Wm ± _Wσ and the range of _Wm ± _1.96Wσ was obtained, and the ratio of the number of test data falling within these ranges to all the test data was calculated. As a result, the RMSE calculated from the deviation between the actual data Wa of the finish exit width _W and the average value _Wm of the finish exit width was good at 0.1 mm. Furthermore, the probability that the finish delivery width W falls within the range of W _m ±W _σ was 67.3%, and the probability that it falls within the range of W _m ±1.96W _σ was 95.3%. This means that if it is assumed that the variation in the finish delivery width W follows a normal distribution, the respective probabilities are 68.3% and 95.0%, and it was confirmed that the variation in the finish delivery width W can be predicted with high accuracy by the width prediction model M of this embodiment. Meanwhile, the width prediction model M generated as described above was stored in the prediction section 112 of the width prediction unit 110, and width control was performed on steel plates with slab widths in the range of 1000 to 1200 mm. In this case, when rough rolling was completed for each rough rolled material and the rough exit width was actually measured by the rough exit width meter 11, the statistical information of the finish exit width was calculated using the width prediction model M, and the operation parameters of the finish rolling mill 6 were reset so that the target width _Wt of the finish exit width W set for each steel plate satisfied the relationship shown in the above formula (1). As the operation parameters of the finish rolling mill 6 to be reset, the tension between rolling stands in the finish rolling mill 6 was selected. The steel plate that had been finish rolled in this way was cooled on the run-out table to produce a hot-rolled steel plate. The hot-rolled steel plate produced was 400 coils. As a result, the ratio of coils whose width was smaller than the target width before the coiler was reduced by 35% in this embodiment compared to the conventional example in which the extra width was set in advance. In addition, the edge cut allowance that was cut off due to the width being larger than the target width before the coiler was reduced by 0.8 mm on average in this embodiment. From the above, it has been confirmed that this embodiment makes it possible to predict statistical information on the width of finish rolled material, and that by applying this to width control of finish rolled material, it is possible to reduce width defects in hot-rolled steel sheets and improve product yield.

Example 2
Another example of the width prediction method for finish rolled material will be described as an embodiment of the present invention. In the above embodiment 1, when the performance data is stored in the database unit 101, the data acquisition unit 103 acquires performance data of the slab thickness, slab width, and slab length, which are information on the slab dimensions, as the attribute information of the slab. In addition, the data acquisition unit 103 acquires performance data of the contents of C, Si, Mn, P, S, Nb, Ti, Cu, Ni, Mo, and B, which are information on the component composition of the slab, as the attribute information of the slab. Then, the performance data of these slab attribute information are accumulated in the database unit 101 as a data set associated with the performance data acquired in embodiment 1 by the data acquisition unit 103.

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

The width prediction model M generated in this embodiment is a width prediction model learned by a Gaussian process regression technique, in which the input data are the actual measured value of the width of the rough rolled material, the operation parameters of the finishing mill, and parameters selected from the attribute information of the slab from the data set accumulated in the database unit 101, and the output data is statistical information on the width of the finish rolled material. The operation parameters of the finishing mill used as the input data are the entry thickness, reduction amount, work roll peripheral speed, work roll diameter, and temperature of the front and tail ends of the steel plate at the entry side of the finishing mill in all rolling stands of the finishing mill 6, as in Example 1. In addition, the parameters of the attribute information of the slab used as the input data are the thickness, width, and length of the slab, which are information on the slab dimensions, and the contents of C, Si, Mn, P, S, Nb, Ti, Cu, Ni, Mo, and B of the slab, which are information on the composition of the slab.

In this embodiment, the hyperparameters of the width prediction model M were identified by a Gaussian process regression method using the learning data. Then, the operational performance data of the test data was input to the prediction section 112 of the width prediction section 110, and the average value Wm and standard deviation Wσ of the finishing exit width W, which is the output of the width prediction model, were obtained. In addition, the RMSE (root mean square error) was calculated from the deviation between the actual data Wa of the finishing exit width W, which is the test data, and the average value Wm. Furthermore, the number of test data in which the actual data Wa of the finishing exit width W falls within the range of Wm±Wσ was obtained, and the ratio of the number of test data falling within these ranges to all test data was calculated.

As a result, according to the generated width prediction model M, the RMSE calculated from the deviation between the actual data Wa of the finishing exit width W and the average value Wm was 0.0 mm. In addition, the probability that the finishing exit width W falls within the range of Wm ± Wσ was 65.3%, which is close to the probability of 68.3% when it is assumed that the variation in the finishing exit width W follows a normal distribution. From the above, it was confirmed that according to the present invention, the average value Wm and standard deviation Wσ of the finishing exit width, which are statistical information of the finishing exit width, can be accurately predicted.

Although the above describes an embodiment of the invention made by the present inventors, the present invention is not limited by the description and drawings that form part of the disclosure of the present invention according to this embodiment. In other words, other embodiments, examples, and operational techniques made by those skilled in the art based on this embodiment are all included in the scope of the present invention.

According to the present invention, it is possible to provide a width prediction method for finish rolled material that can predict statistical information including the width variation of the finish rolled material. Also, according to the present invention, it is possible to provide a width control method for finish rolled material that can accurately control the longitudinal width of the finish rolled material taking into account the width variation of the finish rolled material. Also, according to the present invention, it is possible to provide a manufacturing method for hot rolled steel sheet that can improve the product yield of the hot rolled steel sheet. Also, according to the present invention, it is possible to provide a method for generating a width prediction model for finish rolled material that can generate a width prediction model that predicts statistical information including the width variation of the finish rolled material.

REFERENCE SIGNS LIST 1 Hot rolling line 2 Heating furnace 3 Descaling device 4 Width reduction press device 5 Rough rolling mill 6 Finishing rolling mill 7 Cooling device 8 Coiler (winding machine)
11 Rough exit width meter 12 Finish exit width meter 13 Coiler front width meter (coiler entry width meter)
14 Finishing entry width meter 15 Pass line 16a, 16b, 16c, 16d Camera 61 Crop shear 62a, 62b Work roll 63a, 63b Backup roll 64a, 64b Bearing portion (backup roll chock)
65 Housing 66 Load cell 67 Pressing cylinder 68a, 68b Bearing box (work roll chock)
69 Looper 69a Looper roll 90 Control controller 91 Control computer 92 Host computer 100 Width prediction model generation unit 101 Database unit 102 Machine learning unit 103 Data acquisition unit 110 Width prediction unit 111 Input data acquisition unit M Width prediction model SA Rough rolled material SB Steel plate

Claims (3)

A method for predicting the width of a finish rolled material in a hot rolling line including a heating furnace for heating a slab, a rough rolling mill for rough rolling the heated slab to produce a rough rolled material, and a finish rolling mill for finish rolling the rough rolled material to produce a finish rolled material, the method including a prediction step of predicting statistical information of the width of the finish rolled material using a width prediction model learned by a Gaussian process regression technique, the input data being a set value or an actual value of the width of the rough rolled material and one or more operation parameters selected from the operation parameters of the finish rolling mill, and output data being statistical information of the width of the finish rolled material, the method including a setting step of predicting statistical information of the width of the finish rolled material using the width prediction method for the finish rolled material, and setting one or more operation parameters selected from the operation parameters of the finish rolling mill based on the predicted statistical information so as to reduce the probability that the width of the finish rolled material falls below the target width,
The statistical information on the width of the finish rolled material includes an average value Wm _and a standard deviation Wσ _of the width of the finish rolled material , and the setting step includes a step of setting one or more operational parameters selected from operational parameters of the finish rolling mill so that the target width Wt of the finish rolled material _satisfies the relationship shown in the following mathematical formula (1).

The method of claim 1 , wherein the width prediction model includes one or more parameters selected from attribute information of the slab as input data. A method for producing a hot-rolled steel sheet, comprising the step of producing a hot-rolled steel sheet using the method for controlling width of finish rolled material according to claim 1 or 2 .

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