Strip shape detecting device for metal strip, rolling mill and detecting method

Abstract

The change in the plate wave shape distribution is evaluated with high accuracy even in the case where vibration is generated on the metal strip plate. In each of the divided regions obtained by dividing the reflected light region in the plate width direction into j parts in the obtained image, the most upstream position of the upstream side boundary line position of the reflected light region and the most downstream position of the downstream side boundary line position are found, and with respect to each of the obtained images, the difference between the position data of the most upstream side boundary position and the most downstream side boundary position is calculated for each divided region, the value is set as information corresponding to the maximum rolling direction length of the reflected light region of the kth image, and the information is made to correspond to the central position in the plate width direction of the divided region i. When the value indicating the position in the plate width direction is set as a variable x, the position in the plate width direction of the region in the image is normalized to the range of -1 ≤ x ≤ 1 in the plate width range of the region, the value of the information is taken as an index corresponding to the rolling plate wave shape distribution in the plate width direction obtained from the kth image, a Chebyshev polynomial is applied to find the coefficients, and the first order coefficient C1' is taken as a detection result signal of the rolling plate wave shape distribution of the first order component in the plate width direction of the kth image.

Description

Technical Field

[0001] This invention relates to a sheet shape detection device for metal strips, as well as a rolling mill and detection method. Background Technology

[0002] Patent Document 1 describes a defect detection device and method that can easily determine surface shape defects of metal strip without using a special light source such as a rod. The device includes: a roller with its rotation axis extending along the width direction of the rolled steel sheet to lift the rolled steel sheet upward; a camera that captures an image of the rolled steel sheet lifted upward by the roller, including the lifted area; and a control device that determines surface shape defects of the metal strip based on the image captured by the camera.

[0003] Patent Document 2 describes a metal strip shape determination device, rolling mill, and determination method that are less susceptible to minor disturbances or sudden small obstacles compared to previous methods. The device includes: a camera configured to capture an image of a region containing a strip of metal strip being rolled, reflecting a strip of light transversely along the strip width direction; and an image processing computer that determines the shape of the metal strip based on the image captured by the camera. The image processing computer divides the region in the image into multiple partitions along the strip width direction and sends information corresponding to the distribution of the strip waviness in the rolling direction along the strip width direction as a signal, based on index information representing the size of each partition related to the region.

[0004] Existing technical documents

[0005] Patent documents

[0006] Patent Document 1: Japanese Patent No. 6808888

[0007] Patent Document 2: Japanese Patent No. 7130350 Summary of the Invention

[0008] Regarding the quality of the shape of the metal strip rolled by the rolling mill, such as whether it has a waviness, there are many known techniques that rely on linear or rod-shaped reflected light along the width of the metal strip for judgment.

[0009] The detection method is based on the following: when a part of the plate develops a wavy shape and the shape of the plate changes, the shape of the reflected light, which was originally linear or rod-shaped, is no longer a neat shape, and a part of it will move or shift.

[0010] However, there is a problem: because the area of ​​reflected light in the rolling direction at each position in the width direction of the plate is narrow in linear or rod-shaped illumination, it is significantly affected by subtle interferences caused by small obstacles, which can easily lead to false detection.

[0011] The inventors in this case, when performing detection based on ordinary lighting and utilizing the change in the strip-shaped reflected light area reflected on the surface of the metal strip near the bend of the strip lifted by the tension control looper installed between the mill stands of the rolling production line, as disclosed in Patent Document 1, discovered that the influence of interference could be reduced, and as a technology to further utilize the characteristics of the strip-shaped reflected light area, they conceived of the technology disclosed in Patent Document 2.

[0012] In the technology described in Patent Document 2, Chebyshev polynomials are applied to the distribution of the strip-shaped reflected light region in the width direction, such as the length and area of ​​the strip in the rolling direction, which is reflected on the surface of the metal strip near the bending part of the strip lifted by the tension control looper set between the mill stands of the rolling production line. The coefficients of the Chebyshev polynomials are obtained, and the wave-shaped distribution of the strip in the width direction is judged.

[0013] Thus, the following phenomenon was observed: In actual rolling, when the metal strip vibrates at the looper, the position, length, and area of ​​the reflected light area on the surface of the rolled metal strip are constantly changing, and the reflected light area is not stably retained in the same position.

[0014] Regarding the technology described in Patent Document 2, the inventors of this case have conducted repeated and in-depth research, and the result is that it has been clarified that the technology described in Patent Document 2 cannot cope with the scenario of such variation in the reflected light area.

[0015] The present invention provides a sheet shape detection device for metal strip that can evaluate changes in strip waviness distribution with high accuracy even when the metal strip is vibrating, as well as a rolling mill and detection method.

[0016] This invention includes multiple solutions to the aforementioned problems. One example is a sheet shape detection device for a metal strip, specifically for detecting the shape of a rolled metal strip. The device comprises: a camera configured in a rolling mill to capture an image including a region on the surface of the metal strip being lifted by a looper, the region being a strip-shaped area transversely cut along the width direction by illumination light; and an image processing unit that detects the sheet shape of the metal strip based on the image captured by the camera. The sheet shape detection device is characterized in that the image processing unit numbers the images as 1, 2, 3, ..., k, ... according to the order in which the images are acquired. …In the (k)th image, within each segmented region (i) obtained by dividing the reflected light region into j parts along the width of the plate, for the rolling direction of the pixel coordinates, the upstream position Pumin(k)i is determined among the pixel positions constituting the upstream boundary line of the reflected light region, and the downstream position Pdmax(k)i is determined among the pixel positions constituting the downstream boundary line of the reflected light region, where i = 1 to j. For each of the two or more obtained F images from image number (k-F+1) to image number (k), the upstream position is extracted from the F data from Pumin(k-F+1)i to Pumin(k). The data of the side position is used as the first position data, and it is used as the data of the (k)th image and then set as Pure_min(k)i. The data representing the downstream side position is extracted from the F data from Pdmax(k-F+1)i to Pdmax(k)i and used as the second position data, and it is used as the data of the (k)th image and then set as Pdre_max(k)i. For each segmented region (i), the difference [Pdre_max(k)i-Pure_min(k)i] of the position data in the rolling direction is calculated, and [Pdre_max(k)i-Pure_min(k)i] is set as the value of the (k)th image relative to the reflected light region. The information D(k)i corresponding to the maximum rolling direction length is such that the value of the information D(k)i corresponds to the central position in the plate width direction of the segmented region (i). When the value representing the plate width direction position is set as variable (x), the plate width direction position within the plate width range of the reflected light region in the image is normalized to the range of -1≤x≤1. The j values ​​of the information D(k)i are used as indicators corresponding to the rolled plate waviness distribution in the plate width direction obtained from the (k)th image. It is applicable to change the expression of the plate width direction position to (x), and set it as D(k)i=E(xi), which consists only of the 0th, 1st, 2nd, and 4th degree terms of x, E(x)=C0'+C1'×x+C2'×(2x 2 -1)+C4'×(8x4 -8x 2 +1) All of these Chebyshev polynomials, where -1≤x≤1, are obtained from E(xi) with j values ​​of x (xi), and the coefficients (C0', C1', C2', C4') of the Chebyshev polynomial are sent as the detection result signal of the first-order component of the rolled plate waviness distribution in the width direction of the (k)th image. Here, xi is the value of the center position in the width direction of the segmented region (i) obtained by dividing the reflected light region into j parts along the width direction by (x). In addition, F, i, j, k are integers.

[0017] Invention Effects

[0018] According to the present invention, changes in the strip waviness distribution during rolling can be evaluated with high precision even when the metal strip vibrates. Other issues, structures, and effects beyond those described above will become apparent through the following description of embodiments. Attached Figure Description

[0019] Figure 1 This is a diagram illustrating an example of a rolling mill equipped with a sheet shape detection device for metal strip according to an embodiment of the present invention.

[0020] Figure 2 This is an example of how reflected light from illumination during operation in a rolling mill appears as a roughly rectangular band on the surface of a metal strip at the loop section between stands.

[0021] Figure 3 This is an example of how reflected light from illumination during operation in a rolling mill appears as irregular bands along the width of the strip on the surface of the metal strip at the loop section between the stands.

[0022] Figure 4 This is a diagram representing the case where the leveling amount (Gd - Gw) is defined (Gd = Gw).

[0023] Figure 5 This is a diagram representing the case where the leveling amount (Gd - Gw) is defined (Gd > Gw).

[0024] Figure 6 This is a figure illustrating an example of the relationship between the first-order component (C1') of the Chebyshev coefficient and the leveling amount, using "index A" obtained through previous techniques.

[0025] Figure 7 This is a figure illustrating an example of the relationship between the first-order component (C1') of the Chebyshev coefficient and the leveling amount, using the "index B" obtained through this invention.

[0026] Figure 8This is a diagram illustrating an example of obtaining the maximum length D(k)i of the reflected light region in the rolling direction from the (k)th image in the sheet shape detection device of the embodiment, taking into account the variation of the boundary lines of the upstream and downstream sides of the reflected light region.

[0027] Figure 9 This is a diagram illustrating an example of a method for uniformly dividing the strip in the width direction in a metal strip shape detection device according to an embodiment.

[0028] Figure 10 This is a diagram illustrating an example of a method for unevenly dividing a metal strip in the width direction within a sheet shape detection apparatus according to an embodiment.

[0029] Figure 11 This is a flowchart illustrating the plate shape detection process in the plate shape detection device for metal strips in this embodiment.

[0030] Figure 12 This is an example of a monitor displaying the 0th, 1st, 2nd, and 4th orders of the Chebyshev polynomial x in the sheet shape detection device of the embodiment.

[0031] Explanation of reference numerals in the attached figures

[0032] 1…Metal strip

[0033] 2…Reflected light area

[0034] 2A…Upstream boundary line of the reflected light region

[0035] 2B…Downstream boundary of the reflected light region

[0036] 10…F1 rack

[0037] 11, 21, 31, 41, 51… Press down cylinder

[0038] 12, 22, 32, 42, 52… Load detectors

[0039] 20…F2 rack

[0040] 30…F3 rack

[0041] 40…F4 rack

[0042] 50…F5 rack

[0043] Cameras 61, 62, 63, 64…

[0044] 71, 72, 73, 74… Loop

[0045] 80… Image Processing Computer (Image Processing Department)

[0046] 81…Database

[0047] 82…Control device

[0048] 85…monitor

[0049] 90… communication line

[0050] 100…rolling equipment Detailed Implementation

[0051] use Figures 1 to 12 This invention describes embodiments of the metal strip shape detection device, rolling mill, and detection method of the present invention. It should be noted that in the drawings used in this specification, there are instances where the same or corresponding structural elements are labeled with the same or similar reference numerals, and repeated descriptions of these structural elements are omitted.

[0052] First, use Figures 1 to 3 Describe the overall structure of the rolling equipment, including the sheet shape detection device for metal strip. Figure 1 This is a schematic diagram showing the structure of the metal strip shape detection device and the rolling equipment equipped with the metal strip shape detection device according to this embodiment. Figure 2 and Figure 3 This is an example of how reflected light from illumination during operation in a rolling mill appears as a strip on the surface of a metal strip at the looper between stands.

[0053] Figure 1 The rolling equipment 100 for the rolled metal strip 1 shown includes F1 stand 10, F2 stand 20, F3 stand 30, F4 stand 40, F5 stand 50, cameras 61, 62, 63, 64, loopers 71, 72, 73, 74 for tension control, image processing computer 80, database 81, control device 82, monitor 85, etc.

[0054] These F1 racks 10, F2 racks 20, F3 racks 30, F4 racks 40, F5 racks 50, cameras 61, 62, 63, 64, image processing computer 80, database 81, control device 82, and monitor 85 are connected via communication lines 90.

[0055] The metal strip plate 1 of the present invention is composed of cameras 61, 62, 63, 64, loopers 71, 72, 73, 74, image processing computer 80, and database 81.

[0056] It should be noted that the rolling mill 100 is not limited to... Figure 1 The setup shown has five rolling mill stands, but at least two stands are sufficient.

[0057] Frames F1 (10), F2 (20), F3 (30), F4 (40), and F5 (50) each include upper and lower work rolls, upper and lower support rolls supported by contact with these upper and lower work rolls, pressure cylinders 11, 21, 31, 41, and 51 located above the upper support rolls, and load detectors 12, 22, 32, 42, and 52. Furthermore, a six-stage structure can be configured where intermediate rolls are also provided between each work roll and each support roll.

[0058] Loop 71 is a tension control roller disposed between frame F1 10 and frame F2 20. This loop 71 is configured such that its axis of rotation extends along the width direction of the metal strip 1, allowing the traveling metal strip 1 to be placed on the roller, and is configured to lift and hold the metal strip 1 upwards. Furthermore, the loop 71 may be equipped with a device that applies upward force using a spring, or is lifted by means of a hydraulic cylinder or motor.

[0059] Similarly, the tension control loop 72 is located between frame 20 of F2 and frame 30 of F3, the tension control loop 73 is located between frame 30 of F3 and frame 40 of F4, and the tension control loop 74 is located between frame 40 of F4 and frame 50 of F5.

[0060] The camera 61 is configured to capture an image of the surface of the metal strip 1, including a region known as the reflected light region 2, which is visible on the surface of the rolled metal strip 1 that is lifted and bent upwards by the looper 71. This region is visible due to reflection from a strip of irradiated light transversely along the width direction of the strip. Preferably, the camera 61 is positioned on the outer side of the metal strip 1 in the width direction when viewed from above. The image data captured by the camera 61 is transmitted to the image processing computer 80 via the communication line 90.

[0061] Additionally, camera 62 is positioned to capture images of the surface of the metal strip 1, including a region known as the reflected light region 2, which can be identified on the surface of the rolled metal strip 1 that is lifted and bent upwards from the looper 72. This region is visible due to reflections from a strip of irradiation light that cuts across the width of the strip. Camera 63 is positioned to capture images of the surface of the metal strip 1, including a region known as the reflected light region 2, which can be identified on the surface of the rolled metal strip 1 that is lifted and bent upwards from the looper 73. This region is visible due to reflections from a strip of irradiation light that cuts across the width of the strip. Camera 64 is positioned to capture images of the surface of the metal strip 1, including a region known as the reflected light region 2, which can be identified on the surface of the rolled metal strip 1 that is lifted and bent upwards from the looper 74. This region is visible due to reflections from a strip of irradiation light that cuts across the width of the strip. The image data captured by cameras 62, 63, and 64 is transmitted to image processing computer 80 via communication line 90.

[0062] Like camera 61, cameras 62, 63, and 64 are preferably positioned on the outer side of the metal strip 1 in the width direction when viewed from above.

[0063] These cameras 61, 62, 63, and 64 are used to perform a photographing step, which involves taking an image of the rolled metal strip 1, including the area containing the strip of reflected light that is transversely cut along the width direction of the strip.

[0064] The system can be further equipped with lighting to illuminate the raised shooting area of ​​the metal strip 1, which is mainly captured by cameras 61, 62, 63, and 64 and is lifted upwards from the rollers. This lighting can be ordinary lighting appropriately configured on the ceiling or the like of a rolling mill where the rolling equipment 100 is installed. In this invention, no particularly novel lighting equipment is required, but dedicated lighting can also be provided.

[0065] The image processing computer 80 is an apparatus that performs various processing (including image processing steps) on images captured by cameras 61, 62, 63, and 64 to detect the shape of the metal strip 1. Preferably, the image processing computer 80 is the main body that performs the image processing steps.

[0066] For example, for Figure 2 or Figure 3The image shown, which includes the area near the bent part of the metal strip 1 that is rolled and lifted upward by the loopers 71, 72, 73, 74, i.e. the lifted area, is processed to determine the range including the upstream / downstream boundary of the part where the brightness of the reflected light from the surface of the metal strip 1 reflected in the image is greater than a certain brightness value as the reflected light region 2.

[0067] Here, for the reflected light region 2 of the metal strip 1, where a strip of reflected light can be seen transversely along the width direction, if the wavy distribution along the rolling direction (long side direction of the strip) at each position in the width direction of the metal strip 1 is uniform, then the surface of the metal strip 1 is flat, the strip shape is good, and the steepness is uniform and small in the width direction. Therefore, if... Figure 2 As shown, the difference in the length distribution of the reflected light region 2 in the rolling direction at various locations along the plate width is small. Therefore, for the boundary line of the reflected light region 2 generated by illumination, the interval between the upstream boundary line 2A and the downstream boundary line 2B is approximately uniform and roughly parallel in the plate width direction. When the reflected light region 2 is uniformly divided into multiple partitions along the plate width direction, the area value of each partition, the average length in the rolling direction, and other parameters are approximately uniform in all partitions.

[0068] In contrast, when the wavy pattern in the rolling direction differs depending on the position in the width direction (e.g., edge wavy, center wavy), the metal strip is not flat, has defects in its shape, and its steepness varies in the width direction. Consequently, the areas reflected on the surface of the strip differ, such as... Figure 3 As shown, the boundary line of the reflected light region 2 generated by the illumination will be wavy on one or both of the upstream boundary line 2A and the downstream boundary line 2B, and the interval between the upstream boundary line 2A and the downstream boundary line 2B of the reflected light region 2 will be uneven in the width direction of the plate. Therefore, when the reflected light region 2 is uniformly divided into multiple sections along the width direction of the plate, parameters such as the area value of each section and the average length in the rolling direction become uneven in each section.

[0069] Here, in the aforementioned Patent Document 1, the width direction distribution of the rolling direction length and area of ​​the reflected light region 2 that appears on the surface of the metal strip 1 near the curved portion of the metal strip 1 lifted by the loopers 71, 72, 73, and 74 is used as an index of the plate wave distribution based on rolling, and the Chebyshev polynomial of the following formula (1) is used for curve fitting.

[0070] E(x) = C0' + C1' × x + C2' × (2x) 2 -1)+C4'×(8x 4 -8x 2 +1)(where -1≤x≤1)……(1)

[0071] In the Chebyshev polynomial, for example, as an index of the wavy distribution in the width direction of the rolled strip, E(x) is conceived as the rolling direction length of the reflective light region 2 on the surface of the metal strip 1 at loopers 71, 72, 73, and 74, and represents the size corresponding to the wavy distribution in the width direction of the rolled strip. Furthermore, C0', C1', C2', and C4' represent the values ​​of the coefficients of the 0th, 1st, 2nd, and 4th orders of x obtained by component separation of the Chebyshev polynomial conceived as representing the size corresponding to the wavy distribution in the width direction. X represents the normalized position in the width direction; for example, x = -1 represents the width end position on the drive side (DS), and x = 1 represents the width end position on the working side (WS). That is, in this case, if the coefficient of the first-order component of x (C1') in the Chebyshev polynomial is positive, it indicates that the wavy shape on the working side (WS) is large. Furthermore, if the coefficient of the second-order component of x (C2') is positive, it indicates that the wavy shape at the ends of the plate width is larger than that in the center of the plate width. Additionally, if the coefficient of the fourth-order component of x (C4') is negative, it indicates that the wavy shape in the quarter section of the plate width is large.

[0072] The following is the definition of the leveling quantity.

[0073] like Figure 4 as well as Figure 5 As shown, the leveling amount is defined as the value (Gd-Gw) obtained by subtracting the distance between the upper and lower work roll shafts at the position of the pressing cylinder on the working side (WS) from the distance Gd between the upper and lower work roll shafts at the position of the pressing cylinder on the drive side (DS: Drive Side).

[0074] Assuming the plate thickness at the center of the plate width remains unchanged even when the leveling amount is altered, therefore, if Figure 5 As shown, in the leveling ratio Figure 4 As the state shown increases, the plate thickness on the drive side (DS) becomes thicker, the plate thickness on the working side (WS) becomes thinner, and the plate wavy shape on the working side (WS) becomes larger. The value of the first-order component (C1') of the Chebyshev coefficient obtained by this method is positive when it indicates a large plate wavy shape on the working side (WS), and negative when it indicates a large plate wavy shape on the drive side (DS).

[0075] The reflected light region 2 is divided along the width direction of the plate by a specific number of segments. For example, within each segmented region, the rolling direction length of the reflected light region 2, which serves as an indicator of the plate waviness distribution in the width direction, is averaged. The averaged value is then reset and set as a Chebyshev polynomial E(x) representing the magnitude corresponding to the plate waviness distribution in the width direction. The E(x) obtained here is used as "index A", and the Chebyshev coefficients are obtained using conventional techniques.

[0076] Assuming that intentionally varying the leveling amount of the rolling mill during actual hot rolling would significantly alter the first-order component (C1') of the Chebyshev polynomial coefficients, then... Figure 6 The figure shows the relationship between the first-order component (C1') of the Chebyshev coefficient of index A and the leveling amount, obtained by the index extraction method of previous techniques.

[0077] Such as Figure 6 As shown, it can be confirmed that there is almost no correlation between the change in the leveling amount and the first-order component (C1') of the Chebyshev coefficient obtained from index A and the change in the leveling amount.

[0078] Therefore, it is speculated that in the method of averaging the length in the rolling direction in each segmented region of the reflected light region 2 and extracting it as index A, there is a scenario where the actual change in plate shape cannot be measured. Therefore, the inventors of this case believe that there is still room for improvement in the method of selecting the index.

[0079] It is thus inferred that the vibration of the metal strip 1 was observed at positions 71, 72, 73, and 74 of the looper. The position of the reflected light area 2 projected on the surface of the rolled metal strip and the variation data such as the length and area in the rolling direction were averaged. The Chebyshev coefficient obtained was smoothed, and it became impossible to clearly obtain the correlation between the change in the leveling amount and the first component (C1') of the Chebyshev coefficient with index A.

[0080] That is, considering that the vibration of the metal strip 1 is affected by the rolling-based plate waviness, and whether extracting this effect can reflect the rolling-based plate waviness distribution in the Chebyshev coefficient, the result of this in-depth study is to consider a new index extraction method as described below. This new index obtained by the present invention is designated as "Index B".

[0081] Similarly, assuming that intentionally varying the leveling amount of the rolling mill during actual hot rolling would significantly change the first-order component (C1') of the Chebyshev polynomial coefficients, then... Figure 7 The expression in the figure represents the relationship between the first-order component (C1') of the Chebyshev coefficient obtained through this embodiment and the leveling amount.

[0082] Such as Figure 7 As shown, it can be confirmed that there is a certain degree of correlation between the change in the leveling amount and the change in the first-order component (C1') of the Chebyshev coefficient obtained by the processing of this embodiment described above. In other words, it is believed that the method for extracting index B can extract the influence of the plate waviness caused by rolling.

[0083] Therefore, when determining the strip width direction of the maximum length of the reflected light region 2 reflected on the surface of the metal strip 1 near the bend of the metal strip 1 lifted by the loopers 71, 72, 73, and 74 between the mill stands in the rolling production line, and performing a determination on the strip waviness distribution based on rolling in the strip width direction, it is preferable to use the index B obtained by the processing in this embodiment. The method for extracting index B will be explained next.

[0084] In the image processing computer 80 of this embodiment, for each acquired image, the following two analytical processes are performed. The first analytical process performed by the image processing computer 80 is to label the images as 1, 2, 3, ..., k, ... according to the order in which the images were acquired. In the (k)th image, within each partition (i) (i = 1 to j) obtained by dividing the reflected light region 2 into j parts along the width direction, the rolling direction position Pumin(k)i of the upstream pixel of the pixel constituting the upstream boundary line 2A of the reflected light region 2 in the rolling direction is determined. Similarly, the rolling direction position Pdmax(k)i of the downstream pixel of the pixel constituting the downstream boundary line 2B of the reflected light region 2 in the rolling direction is determined. This data is stored in the database 81.

[0085] The second parsing process performed by the image processing computer 80 is as follows: for each of the F images stored in the database 81 from image number (k-F+1) to image number (k), the first position data that is the upstream position in the rolling direction is extracted from the F data from Pumin(k-F+1)i to Pumin(k)i within the partition of the segmentation region (i), and this data is set as Pure_min(k)i as the data of the (k)th image. In addition, the second position data that is the downstream position in the rolling direction is extracted from the F data from Pdmax(k-F+1)i to Pdmax(k)i within the partition of the segmentation region (i), and this data is set as Pdre_max(k) as the data of the (k)th image. These data are stored in the database 81.

[0086] For each segmented region (i), calculate the difference [Pdre_max(k)i - Pure_min(k)i] of the position data in the rolling direction. Use the obtained j values ​​of [Pdre_max(k)i - Pure_min(k)i] as the index B (maximum length in the rolling direction of the reflected light region 2) corresponding to the wavy shape of the rolled plate in the (k)th image, and represent it as D(k)i. Align this with the central position of each segmented region (i) in the plate width direction. When setting the value representing the plate width direction position as variable (x), set the D(k)i corresponding to the position x that normalizes the plate width direction position within the plate width range to the range -1 ≤ x ≤ 1 as E(xi) of the (k)th image. It should be noted that xi is the value representing the central position in the plate width direction of the segmented region (i) expressed by (x).

[0087] For each segmented region (i), the image processing computer 80 applies the values ​​of the central position xi and E(xi) (E(xi) = D(k)i) of each segmented region (i) in the width direction of the (k)th image to the Chebyshev polynomial of equation (1), and uses the least squares method to obtain the coefficients (C0', C1', C2', C4') of the Chebyshev polynomial from the equation of its approximate curve. The first-order coefficient (C1') is sent as the detection result signal of the first-order component of the rolled plate waviness distribution in the width direction.

[0088] like Figure 8 As shown, the maximum length D(k)i of the reflected light region 2 in the rolling direction is a value that makes the value of [Pdre_max(k)i - Pure_min(k)i] obtained in each segmented region (i) correspond to the central position of each segmented region (i) in the plate width direction.

[0089] Furthermore, preferably, the image processing computer 80 can also send any one or more of the second-order coefficients (C2') or fourth-order coefficients (C4') as detection result signals of the second-order or fourth-order components of the rolled plate waviness distribution in the plate width direction, based on the first-order coefficient (C1').

[0090] Database 81 also functions as a recording medium, which records various parameters used when the rolling equipment 100 is operated.

[0091] In this embodiment, when k≥F and k and F are integers, the database 81 can store the first position data Pure_min(k)i (i=1~j) and the second position data Pdre_max(k)i (i=1~j) in the rolling direction for each of the F images obtained consecutively from the (k-F+1)th image to the (k)th image, and for each of the reflected light area 2 that will be projected on the surface of the metal strip and divided into j partitions (i) along the width direction.

[0092] Here, regarding the method for segmenting the reflected light region 2, the segmented regions (i) (i = 1 to j) obtained by dividing the plate into j parts along the width direction can be, for example: Figure 9 As shown, it can be uniformly divided into j parts, or it can be, as shown in the example. Figure 10 As shown, each segment is divided into j segments with an arbitrary width and uneven distribution.

[0093] return Figure 1 The control device 82 is a device that controls the operation of each device in the rolling equipment 100. In this embodiment, it is a device that performs various controls in the image processing computer 80 corresponding to the detection of the shape of the metal strip 1.

[0094] These image processing computers 80, databases 81, and control devices 82 can be configured as computers having monitors 85 such as liquid crystal displays (described later), input devices, storage devices, CPUs, memory, etc. They can be configured as a single computer or as different computers, without particular limitation.

[0095] The control of the actions of each device based on the image processing computer 80 and the control device 82 is performed according to various programs recorded in the storage device. Furthermore, the control processing of actions performed by the image processing computer 80 and the control device 82 can be summarized in a single program, distributed among multiple programs, or a combination thereof. Additionally, some or all of the programs can be implemented in dedicated hardware, or they can be modularized.

[0096] The monitor 85 is a display device such as a monitor or an audio device such as an alarm. For example, it is a device used to communicate the operator's response when the image processing computer 80 detects a problem with the board shape. Therefore, as such a monitor 85, a monitor is mostly used.

[0097] Here, the image processing computer 80 described above includes a display signal unit that sends signals related to the content displayed on the monitor 85 to the control device 82 and the monitor 85.

[0098] The operator can confirm the status of the plate shape by visually observing the display screen of the monitor 85 and the individual racks and the racks in relation to each other during the operation.

[0099] Furthermore, it is not limited to the method of automatically improving the board shape by means of the control device 82 while communicating the board shape problem to the operator; it can be set to a method of displaying only on the monitor 85, or to a method of omitting the display to the monitor 85 and automatically improving the board shape problem by means of the control device 82.

[0100] Next, use Figure 11 and Figure 12 This invention describes the process of the plate shape detection device and detection method for the rolled metal strip 1.

[0101] exist Figure 11 The flowchart illustrates the calculation method of the indicators of this invention.

[0102] like Figure 11 As shown, before or during rolling, the image processing computer 80 sets the number of images F (e.g., F = 20) for determining the maximum rolling direction length of the reflected light region 2 (step S201) and sets the image number k (step S202). Here, the initial value of the image number is set to k = 1.

[0103] Then, the image processing computer 80 obtains surface images (image number k) of the metal strip 1 near the bend of the metal strip 1 lifted by the loopers 71, 72, 73, and 74, captured by the cameras 61, 62, 63, and 64 (step S203). Here, the obtained images are numbered 1, 2, 3, ..., k, ... in the order of acquisition.

[0104] Next, the image processing computer 80 performs image processing on the images (image number k) captured by the cameras 61, 62, 63, and 64 to extract the reflected light region 2 on the surface of the metal strip 1 near the curved part of the metal strip 1 (step S204).

[0105] For example, the image processing computer 80 performs binarization processing on all pixels (pixels) reflected in the selected rolling surface image range in the images captured by the cameras 61, 62, 63, and 64 to determine an appropriate threshold for brightness. From this, it determines the pixel coordinates constituting the upstream boundary line 2A and the downstream boundary line 2B along the width direction of the reflected light region 2 projected on the surface of the metal strip, thus defining the reflected light region 2. The details can be set using known methods.

[0106] Next, the image processing computer 80 will divide the reflected light region 2 extracted from the image (k) captured by the cameras 61, 62, 63, and 64 into j parts along the width direction of the plate (e.g., j = 7) (step S205).

[0107] Next, within each segmented region (i) (i = 1 to j) of the reflected light region 2 extracted from the images (k) captured by cameras 61, 62, 63, and 64, the image processing computer 80 selects the pixel located in the upstream rolling direction from the pixel positions of the upstream boundary line 2A constituting the reflected light region 2, sets the rolling direction pixel position as "Pumin(k)i" and preferably saves it in the database 81 (step S206), and selects the pixel located in the downstream rolling direction from the pixel positions of the downstream boundary line 2B constituting the reflected light region 2, sets its rolling direction pixel position as "Pdmax(k)i" and preferably saves it in the database 81 (step S207). These steps S206 and S207 can be performed in different orders, simultaneously, or step S207 can be performed before step S206.

[0108] Furthermore, the image processing computer 80 determines whether the image number is k < F (step S208). If it determines that the image number is k < F, the process proceeds to step S209, updates the image number k (k = k + 1) (step S209), and then proceeds to step S203, waiting for the processing of a predetermined number of images to be executed. Conversely, if it determines in step S208 that the image number is k ≥ F, the process proceeds to step S210.

[0109] Next, for each segmented region (i) of the reflected light region 2, the image processing computer 80 compares the “Pumin(k)i” saved in step S206 above with the number of images F from image number (k-F+1) to image number (k), extracts the pixel position representing the upstream position again, and saves it as “Pure_min(k)i” in the database 81 (step S210). It also compares the “Pdmax(k)i” saved in step S207 above with the number of images F from image number (k-F+1) to image number (k), extracts the pixel position representing the downstream position again, and saves it as “Pdre_max(k)i” in the database 81 (step S211).

[0110] Here, the rolling direction position of the pixel coordinates in the image increases from the upstream side to the downstream side. Thus, in the segmented region (i), the upstream position among the upstream boundary line positions is recorded as "Pure_min(k)i", and the downstream position among the downstream boundary line positions is recorded as "Pdre_max(k)i".

[0111] Specifically, in Table 1 below (example of resetting the first position data (Pure_min(k)i) and the second position data (Pdre_max(k)i), and an example of extracting index B), when the number of images is set to f, a database 81 is defined as taking the images from the (k-f+1)th image to the (k)th image as objects, and storing the upstream and downstream data of each image when the reflected light region 2 is divided into j partitions. In each partition, the first position data and the second position data are further reset from the f images, and the first position data is subtracted from the second position data, set as D(k)i = [Pdre_max(k)i] - [Pure_min(k)i]. In this invention, this value D(k)i is set as index B with respect to the kth image. Furthermore, the table display of Pure_min(k)i and Pdre_max(k)i is just an example. In Table 1, the bold text "Pumin" represents the data at the upstream position of the Pumin values ​​of the f images from the (k-f+1)th image to the (k)th image, and the bold text "Pdmax" represents the data at the downstream position of the Pdmax values ​​of the f images from the (k-f+1)th image to the (k)th image.

[0112] Table 1

[0113]

[0114] For example, in the case shown in Table 1, within the first partition of the segmented region i=1 within the j partitions that divide the reflected light region 2 along the width of the plate, the pixel in the upstream rolling direction among the pixel positions of the upstream side boundary line 2A constituting the reflected light region 2 is selected. This rolling direction position is set as Pumin(k)1 for the k-th image. However, in the f-th image which is the evaluation object, the expression is changed to Pumin(1)1 for the (k-f+1)-th image and to Pu for the (k-f+2)-th image. min(2)1, for the (k-f+3)th image, change the expression to Pumin(3)1, ..., for the kth image, change the expression to Pumin(f)1. When the upstream position of Pumin(1 / ... / f)1 in these f images is Pumin(1)1 in the (k-f+1)th image, use the upstream rolling direction position, i.e., Pumin(1)1, as the upstream rolling direction position when image number k and set it to "Pure_min(k)1" and save it.

[0115] Similarly, within the first partition of the segmented region i=1, the pixel in the downstream rolling direction among the pixels that constitute the downstream side boundary line 2B of the reflected light region 2 is selected, and this rolling direction position is set as Pdmax(k)1 for the k-th image. However, in the f-th image which is the evaluation object, for the (k-f+1)-th image, the expression is changed to Pdmax(1)1, for the (k-f+2)-th image, the expression is changed to Pdmax(2)1, and for the (k-f)-th image, the expression is changed to Pdmax(2)1. +3) images, change the description to Pdmax(3)1……, for the kth image, change the description to Pdmax(f)1, when the downstream position of Pdmax(1 / …… / f)1 among these f images is Pdmax(3)1 in the (k-f+3)th image, use the downstream rolling direction position, i.e. Pdmax(3)1, as the downstream rolling direction position when image number k and set it to "Pdre_max(k)1" and save it.

[0116] Similarly, within the second region of segmentation region i=2, the pixel at the uppermost rolling direction among the pixels constituting the upstream boundary line 2A of the reflected light region 2 is selected. This rolling direction position is set as Pumin(k)2 for the k-th image. However, in the f images that are the evaluation objects, for the (k-f+1)-th image, the expression is changed to Pumin(1)2; for the (k-f+2)-th image, the expression is changed to Pumin(2)2; for the (k-f+3)-th image, the expression is changed to Pumin(3)2; ..., for the k-th image, the expression is changed to Pumin(f)2. Among the Pumin(1 / ... / f)2 of these f images, the uppermost... When the upstream position is Pumin(1)2 in the (k-f+1)th image, the upstream position, namely Pumin(1)2, is used as the upstream rolling direction position when the image number is k, and then set to "Pure_min(k)2" and saved. When the downstream position of the pixel position of the downstream side boundary line 2B of the reflected light area 2 is Pdmax(1 / ... / f)2, the downstream position of the pixel position in the downstream rolling direction is Pdmax(2)2 in the (k-f+2)th image, the downstream position, namely Pdmax(2)2, is used as the downstream rolling direction position when the image number is k, and then set to "Pdre_max(k)2" and saved.

[0117] Reset "Pure_min(k)i" and "Pdre_max(k)i" from segmentation region i=1 to segmentation region i=j.

[0118] Next, the image processing computer 80 calculates the difference between the downstream position "Pdre_max(k)i" extracted again at the downstream boundary line 2B and the upstream position "Pure_min(k)i" extracted again at the upstream boundary line 2A in each segmented region (i) of the reflected light region 2 at the time point of the camera image (k) obtained from the above steps S210 and S211, and uses it as the maximum rolling direction length of the reflected light region 2 "D(k)i=[Pdre_max(k)i]-[Pure_min(k)i]" (step S212).

[0119] Next, the image processing computer 80 re-marks the center position of the plate width direction of each segmented region (i) when the reflected light region 2 is divided along the plate width direction using the variable (x) of the plate width direction position in each segmented region (i). This makes the maximum rolling direction length "D(k)i" of the reflected light region 2 in each segmented region (i) obtained at the time point of the camera image (k) obtained in step S212 correspond to the center position (xi) in the plate width direction of the segmented region (i). The E(xi) marked by (x) as E(xi) = D(k)i is curve-fitted with the Chebyshev polynomial of equation (1), and the Chebyshev coefficients (C0', C1', C2', C4') are calculated from the obtained approximation (step S213).

[0120] Next, the image processing computer 80 sends the Chebyshev coefficients (C1', C2', C4') obtained in step S213, for example, to the control device 82 and the monitor 85 as the detection result signal of the wavy distribution in the k-th image (step S214).

[0121] Then, the image processing computer 80 determines whether rolling is continuing (step S215). If it determines that rolling is continuing, the processing returns to step S209 and continues the plate shape detection processing. Conversely, if it determines that rolling is complete, the processing ends.

[0122] It should be noted that this embodiment does not use the third-order component for the Chebyshev polynomial. This is because the rolling control mechanism of the rolling mill does not correspond to the plate wavy shape correction of the third-order component. By omitting the calculation and corresponding means of the third-order component, it is easier to judge the condition of the rolled plate shape and correct the plate wavy shape of the separated first-order, second-order, and fourth-order components.

[0123] The image processing computer 80 can output control command signals to the control device 82 to correct leveling, bending force, and pairwise cross angles based on the polynomial approximation result in the plate width direction obtained using the Chebyshev polynomial of equation (1). Moreover, by outputting display command signals to the monitor 85 instead, or based thereon, to guide the display required for correcting leveling, bending force, and pairwise cross angles, correction information for leveling, bending force, and pairwise cross angles can be conveyed to the operator.

[0124] Preferably, the image processing computer 80 is capable of displaying the 0th-order component [C0'], 1st-order component [C1'×x], and 2nd-order component [C2'×(2x)] of the function representing the vectors of each degree term (C0', C1', C2', C4') in the Chebyshev polynomial E(x) of equation (1) above. 2 -1)], 4th order component [C4'×(8x 4 -8x 2 The signal is sent to the monitor 85 in the form of a graph of each component of +1). The image displayed on the monitor 85 becomes, for example... Figure 12 The scene shown.

[0125] Figure 12 This is an example diagram showing the display screen of monitor 85. Figure 12 The example shown uses the positions along the width of the plate (−1 ≤ x ≤ 1) to represent the distribution of the 0th, 1st, 2nd, and 4th degree components of a Chebyshev polynomial. The operator confirms this. Figure 12 The monitor 85 shown can perform operations such as leveling, bending force, and pair cross angle (in the case of pair cross rolling mills) to make corrections.

[0126] The first-order component coefficient (C1') in the Chebyshev polynomial coefficients of equation (1) represents the index of the unilateral wave. Therefore, the leveling of the pressing cylinder 41 on the upstream drive side (DS) and working side (WS) of the corresponding camera 64, and / or the pressing cylinder 51 on the downstream drive side (DS) and working side (WS) is operated to output an operation command signal to the control device 82 in a manner that normalizes the first-order component (within the target range).

[0127] The quadratic component coefficient (C2') in the Chebyshev polynomial coefficients of equation (1) represents the index of double-sided wave or intermediate wave. Therefore, one or more of the following operations are performed. An operation command signal is output to the control device 82 in a manner that operates the bending device of the work roll / intermediate roll of the upstream mill (F4 stand 40) and / or the downstream mill (F5 stand 50) corresponding to the camera 64. In the case of a pair of cross mills, an operation command signal is output to the control device 82 in a manner that operates the pair of cross angles. In the case of a work roll shifting / intermediate roll shifting mill, since it is difficult to shift during rolling, the intermediate wave / double-sided wave is predicted in advance and an operation command signal is output to the control device 82 in a manner that operates the shifting operation of the work roll / intermediate roll, thereby normalizing the quadratic component (within the target range).

[0128] The fourth-order component coefficient (C4') in the Chebyshev polynomial coefficients of equation (1) represents the index of the quarter wave. Therefore, to correct the quarter wave, one or more of the following operations are performed. The bending operation of the bending device of the work rolls of the upstream mill (F4 stand 40) and / or the downstream mill (F5 stand 50) corresponding to the camera 64 is performed. Furthermore, in the case of a pair of cross mills, the pair of cross angles are operated together with the bending operation or separately. In the case of a six-stage intermediate roll shifting mill, the quarter wave is predicted in advance, and the intermediate rolls are shifted to the correct position. An operation command signal is output to the control device 82 in such a way as to perform the bending operation and the pair of cross angle operation, thereby normalizing the fourth-order component representing the quarter wave (so that it is within the target range in a way that becomes the shape of the target plate). It should be noted that, regarding the quarter wave, the smaller the roll diameter is relative to the roll length, the easier it is for the roll to bend in the area at the end of the roll width due to the bending operation, thereby easily generating a quarter wave, but it can be normalized by the above operation.

[0129] Next, the effects of this embodiment will be explained.

[0130] In the metal strip 1 shape detection device of the rolling mill described above, the image processing computer 80 labels the images as 1, 2, 3, ..., k, ... according to the image acquisition order. In the (k)th image, in each segmented region (i) (i = 1 to j) obtained by dividing the reflected light region 2 into j parts along the width direction, the upstream position Pumin(k)i is calculated among the pixel positions constituting the upstream side boundary line of the reflected light region 2, and the downstream position is calculated among the pixel positions constituting the downstream side boundary line of the reflected light region 2. For each of the F images obtained from image number (k-F+1) to image number (k), at position Pdmax(k)i, data representing the upstream position is extracted from the F data from Pumin(k-F+1)i to Pumin(k)i and used as the first position data, and this is set as Pure_min(k)i for the data of the (k)th image. Data representing the downstream position is extracted from the F data from Pdmax(k-F+1)i to Pdmax(k)i and used as the second position data. This is then used as the data for the (k)th image and set as Pdre_max(k)i. For each segmented region (i), the difference in position data in the rolling direction [Pdre_max(k)i - Pure_min(k)i] is calculated. [Pdre_max(k)i - Pure_min(k)i] is set as the information D(k)i corresponding to the maximum rolling direction length of the reflected light region in the (k)th image, making it correspond to the center position in the plate width direction of the segmented region (i). When the value representing the plate width direction position is set as variable (x), the reflected light in the image is... The plate width direction position within the plate width range of the reflected light region 2 is normalized to the range of -1≤x≤1. The maximum rolling direction length D(k)i=[Pdre_max(k)i-Pure_min(k)i] of the reflected light region 2 is used as an index corresponding to the rolled plate waviness distribution in the plate width direction obtained from the (k)th image. The expression of the plate width direction position is changed to (x), and set as D(k)i=E(xi), consisting only of the 0th, 1st, 2nd, and 4th degree terms of x, that is, E(x)=C0'+C1'×x+C2'×(2x 2 -1)+C4'×(8x 4 -8x 2+1) All of this is a Chebyshev polynomial, where -1 ≤ x ≤ 1. From E(xi) with j values ​​of x (xi), the coefficients (C0', C1', C2', C4') of the Chebyshev polynomial are obtained through curve fitting (curve approximation), and its first-order coefficient (C1') is sent as the detection result signal of the first-order component of the rolled plate waviness distribution in the plate width direction of the (k)th image. Here, xi is expressed by (x) as the value of the central position in the plate width direction of the segmented region (i) obtained by dividing the reflected light region 2 into j parts along the plate width direction. It should be noted that in the normalized plate width direction position (x) of -1 ≤ x ≤ 1, for example, x = -1 represents the position of the plate width end on the driving side, x = 0 represents the position of the plate width center, and x = 1 represents the position of the plate width end on the working side. In addition, F, i, j, and k are integers.

[0131] Therefore, it is possible to evaluate with high precision the changes in the wave-shaped distribution that cannot be addressed by the aforementioned patent document 1.

[0132] In addition, the image processing computer 80 further sends one or more of the first-order coefficients (C1'), second-order coefficients (C2'), or fourth-order coefficients (C4') as detection result signals of the first-order, second-order, or fourth-order components of the rolled plate waviness distribution in the plate width direction, thereby enabling it to handle more plate shape variations.

[0133] <Other>

[0134] Furthermore, the present invention is not limited to the above embodiments and can be modified and applied in various ways. The above embodiments have been described in detail for ease of understanding of the present invention and are not limited to having all the structures described.

Claims

1. A sheet shape detection device for metal strip, comprising: A camera, configured in the rolling mill, is used to capture images of a region known as a reflected light area, which can be identified on the surface of a metal strip lifted by a looper. The region is a strip-shaped area transversely across the width of the strip and reflected by illumination light. The image processing unit detects the shape of the metal strip based on the image captured by the camera. The metal strip shape detection device is characterized in that... The image processing unit labels the images as 1, 2, 3, ..., k, ... according to the order in which the images were acquired. In the (k)th image, within each segmented region (i) obtained by dividing the reflected light region into j parts along the width of the plate, for the rolling direction of the pixel coordinates, the upstream position Pumin(k)i is calculated among the pixel positions constituting the upstream boundary line of the reflected light region, and the downstream position Pdmax(k)i is calculated among the pixel positions constituting the downstream boundary line of the reflected light region, wherein... i = 1 ~ j, For each of the F images obtained from image number (k-F+1) to image number (k), extract the data representing the upstream position from the F data from Pumin(k-F+1)i to Pumin(k)i and use it as the first position data, and then use it as the data of the (k)th image and set it as Pure_min(k)i. Extract the data representing the downstream position from the F data points up to Pdmax(k-F+1)i to Pdmax(k)i and use it as the second position data. Then, use this data as the data for the (k)th image and set it as Pdre_max(k)i. For each segmented region (i), calculate the difference in position data along the rolling direction [Pdre_max(k)i - Pure_min(k)i]. Set [Pdre_max(k)i - Pure_min(k)i] as the information D(k)i corresponding to the maximum rolling direction length of the reflected light region in the (k)th image, so that the value of the information D(k)i corresponds to the center position along the width direction of the segmented region (i). When the value representing the position in the width direction is set as variable (x), the position in the width direction within the width range of the reflected light area in the image is normalized to the range of -1≤x≤1. The j values ​​of the information D(k)i are used as indices corresponding to the rolled plate waviness distribution in the width direction obtained from the (k)th image. The expression of the position in the width direction is changed to (x), and set as D(k)i=E(xi), consisting only of the 0th, 1st, 2nd, and 4th degree terms of x, E(x)=C0'+C1'×x+C2'×(2x 2 -1)+C4'×(8x 4 -8x 2 +1) All of this is better than the Shchev polynomial, where -1 ≤ x ≤ 1. The coefficients (C0', C1', C2', C4') of the Chebyshev polynomial are obtained from E(xi) with j x values ​​(xi), and the coefficient of its first-order term (C1') is sent as the detection result signal of the first-order component of the rolled plate waviness distribution in the plate width direction of the (k)th image. Here, xi is the value of the center position in the width direction of the segmented region (i) obtained by dividing the reflected light region into j parts along the width direction of the plate, as expressed by (x). In addition, F, i, j, and k are integers.

2. The metal strip shape detection device according to claim 1, characterized in that, The image processing unit further sends one or more of the coefficients, either the second-order coefficient (C2') or the fourth-order coefficient (C4'), as a detection result signal of the wavy distribution of the rolled plate in the second-order or fourth-order component in the plate width direction.

3. A rolling mill, characterized in that, have: The metal strip shape detection device according to claim 1 or 2; and Control device, Based on the detection result signal, the control device sends one or more operation signals related to the leveling amount, bending force, or paired cross angle of the rolling mill.

4. A method for detecting the shape of a metal strip, specifically a method for detecting the shape of a rolled metal strip, comprising: The imaging step involves capturing an image using a camera within a rolling mill. The image includes a region on the surface of the metal strip lifted by a looper, defined as a reflected light area, which is the region reflected by a strip of illumination light transversely along the strip's width. The image processing step detects the shape of the metal strip based on the image captured in the shooting step. The method for detecting the shape of the metal strip is characterized in that... In the image processing step, The images are numbered 1, 2, 3, ..., k, ... according to the order in which they were acquired. In the (k)th image, within each segmented region (i) obtained by dividing the reflected light region into j parts along the width of the plate, for the rolling direction of the pixel coordinates, the upstream position Pumin(k)i is calculated among the pixel positions constituting the upstream boundary line of the reflected light region, and the downstream position Pdmax(k)i is calculated among the pixel positions constituting the downstream boundary line of the reflected light region, wherein... i = 1 ~ j, For each of the F images obtained from image number (k-F+1) to image number (k), extract the data representing the upstream position from the F data from Pumin(k-F+1)i to Pumin(k)i and use it as the first position data, and then use it as the data of the (k)th image and set it as Pure_min(k)i. Extract the data representing the downstream position from the F data points up to Pdmax(k-F+1)i to Pdmax(k)i and use it as the second position data. Then, use this data as the data for the (k)th image and set it as Pdre_max(k)i. For each segmented region (i), calculate the difference in position data along the rolling direction [Pdre_max(k)i - Pure_min(k)i]. Set [Pdre_max(k)i - Pure_min(k)i] as the information D(k)i corresponding to the maximum rolling direction length of the reflected light region in the (k)th image, so that the value of the information D(k)i corresponds to the center position along the width direction of the segmented region (i). When the value representing the position in the width direction is set as variable (x), the position in the width direction within the width range of the reflected light area in the image is normalized to the range of -1≤x≤1. The j values ​​of the information D(k)i are used as indices corresponding to the rolled plate waviness distribution in the width direction obtained from the (k)th image. The expression of the position in the width direction is changed to (x), and set as D(k)i=E(xi), consisting only of the 0th, 1st, 2nd, and 4th degree terms of x, E(x)=C0'+C1'×x+C2'×(2x 2 -1)+C4'×(8x 4 -8x 2 +1) All of this is better than the Shchev polynomial, where -1 ≤ x ≤ 1. The coefficients (C0', C1', C2', C4') of the Chebyshev polynomial are obtained from E(xi) with j x values ​​(xi), and the coefficient of its first-order term (C1') is sent as the detection result signal of the first-order component of the rolled plate waviness distribution in the plate width direction of the (k)th image. Here, xi is the value of the center position in the width direction of the segmented region (i) obtained by dividing the reflected light region into j parts along the width direction of the plate, as expressed by (x). In addition, F, i, j, and k are integers.

Images