Rolling mill spindle abnormality diagnosis device, method and program

Abstract

To more accurately diagnose abnormality of a spindle of a roll included in a rolling mill.SOLUTION: In a rolling mill for rolling a metal plate, when rolling the metal plate using the rolling mill including a roll used for rolling the metal plate and a chock supporting the roll, measurement data showing force applied to the chock in a rolling direction which is periodically measured is acquired, a correction coefficient which is a coefficient in a corrected self-regressive model is determined based on the acquired measurement data, and an abnormality of a spindle used for rotation of the roll is diagnosed based on the determined correction coefficient.SELECTED DRAWING: Figure 11

Description

[Technical field]

[0001] The present invention relates to Abnormality diagnosis device for rolling mill spindles, The present invention relates to a method and a program. [Background technology]

[0002] There is a technique for diagnosing abnormalities that occur in rolling mills used for rolling metal sheets. Patent Document 1 discloses an equipment diagnosis method for a plate rolling mill in which a resultant force of the horizontal component of the load vector applied to the rolls of the rolling mill is calculated from the load detection values ​​from the load detection devices of each divided backup roll, and if the calculated resultant force value exceeds a preset allowable range, the occurrence of a failure in the load detection device of each divided backup roll is detected. Moreover, Patent Document 2 discloses diagnosing abnormalities in a rolling mill using an AR model. Furthermore, Patent Document 3 discloses an analysis means for diagnosing an abnormality based on a signal from at least one AE sensor that detects elastic waves generated in an abnormality diagnosis device, and for analyzing an abnormality in a spindle based on the elastic waves detected by the AE sensor. Moreover, Patent Document 4 discloses a modified autoregressive model that is an improvement over the autoregressive model. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 7-265920 [Patent Document 2] JP 2003-106946 A [Patent Document 3] JP 2012-47639 A [Patent Document 4] JP 2018-163135 A Summary of the Invention [Problem to be solved by the invention]

[0004] There is a demand for a more accurate diagnosis of abnormalities in the spindles of rolls included in rolling mills. However, Patent Document 1 is a technology for diagnosing a load detection device, and cannot diagnose abnormalities in the spindles that are connected to the rolls included in the rolling mill and used to rotate the rolls. Furthermore, Patent Documents 2 and 3 have limitations in the accuracy of diagnosis due to the influence of noise contained in the sound and vibration data used for diagnosis. An object of the present invention is to more accurately diagnose abnormalities in a spindle that is connected to a roll included in a rolling mill and used to rotate the roll. [Means for solving the problem]

[0005] The present invention Rolling mill spindle abnormality diagnostic devicea rolling mill for rolling a metal plate, the rolling mill including a roll used for rolling the metal plate and a chock supporting the roll, and includes: an acquisition means for acquiring measurement data indicating a force in a rolling direction applied to the chock, the measurement data being periodically measured when the metal plate is rolled using the rolling mill; a decision means for determining a correction coefficient, which is a coefficient in a modified autoregressive model, based on the measurement data acquired by the acquisition means; and a diagnosis means for diagnosing an abnormality in the spindle, which is connected to the roll and is used for rotating the roll, based on the correction coefficient determined by the decision means, the modified autoregressive model is an equation expressing a predicted value of the measurement data using actual values ​​of the measurement data and the correction coefficient for the actual values, and the decision means is The correction coefficients are determined using an equation in which a first matrix derived from a diagonal matrix having eigenvalues ​​of an autocorrelation matrix derived by singular value decomposition of an autocorrelation matrix derived from measurement data as diagonal components and an orthogonal matrix having eigenvectors of the autocorrelation matrix as column components is used as a coefficient matrix and an autocorrelation vector derived from the measurement data is a constant vector, the autocorrelation vector is a vector having autocorrelation of the measurement data from a time difference of 1 to m which is the number of the actual values ​​used in the corrected autoregressive model as components, the autocorrelation matrix is ​​a matrix having autocorrelation of the measurement data from a time difference of 0 to m-1, and the first matrix is ​​a second matrix Σ derived from s eigenvalues ​​of the autocorrelation matrix and the diagonal matrix for s which is a set number equal to or greater than 1 and less than m. s and a third matrix U derived from the s eigenvalues ​​and the orthogonal matrix. s and the matrix U derived from s Σ s U s T the second matrix is ​​a submatrix of the diagonal matrix and has the s eigenvalues ​​as diagonal components, and the third matrix is ​​a submatrix of the orthogonal matrix and has eigenvectors corresponding to the s eigenvalues ​​as column component vectors. Effect of the Invention

[0006] According to the present invention, it is possible to more accurately diagnose abnormalities in a spindle that is connected to a roll included in a rolling mill and used to rotate the roll. [Brief description of the drawings]

[0007] [Figure 1] FIG. 1 is a diagram illustrating an example of a rolling mill. [Diagram 2] FIG. 2 is a diagram illustrating an example of a rolling mill. [Diagram 3] FIG. 3 is a diagram illustrating an example of a distribution of eigenvalues. [Figure 4] FIG. 4 shows the experimental results. [Diagram 5] FIG. 5 shows the experimental results. [Figure 6] FIG. 6 shows the experimental results. [Figure 7] FIG. 7 shows the experimental results. [Figure 8] FIG. 8 is a diagram illustrating an example of a hardware configuration of an information processing device. [Figure 9] FIG. 9 is a diagram illustrating an example of a functional configuration of an information processing device. [Figure 10] FIG. 10 is a flowchart illustrating an example of processing by the information processing device. [Figure 11] FIG. 11 is a flowchart illustrating an example of processing by the information processing device. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0008] <Embodiment 1> Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

[0009] (Overview of the processing of this embodiment) The information processing device 800 of this embodiment diagnoses abnormalities in a spindle connected to a work roll of a rolling mill, using the technique of a modified autoregressive model (hereinafter referred to as a modified autoregressive model) disclosed in Patent Document 4. A work roll is a roll that directly rolls a metal plate in a rolling mill. Abnormalities in the spindle include a flawed state, a cracked state, a broken state, a deformed state, a worn state, a combination of these states, and the like.

[0010] (Modified autoregressive model) Here, the modified autoregressive model disclosed in Patent Document 4 will be described. The value corresponding to a certain time k (1≦k≦M) in the time series data y is y k M is a number that indicates the time up to which the time series data y includes data. y k An autoregressive model that approximates is, for example, as shown in the following formula 1. As shown in formula 1, an autoregressive model is a prediction value y^ of data at a certain time k (m+1≦k≦M) in time series data. k (In the formula, ^ is written above y) is the actual value y of the data for the time kl (1≦l≦m) prior to that time in the time series data. k-l This is an equation expressed using:

[0011]

number

[0012] In Equation 1, α is the coefficient of the autoregressive model. Also, m is the value of the time series data y at a certain time k in the autoregressive model. k is an integer less than M that indicates how much past data prior to that time should be used to approximate. Next, we use the least squares method to find the predicted value y^ using the autoregressive model. k is the actual value y k Find the conditional expression to approximate the predicted value y^ using the autoregressive model. k is the actual value y kAs a condition for approximating y^ given by Eq. k andy k In this experiment, we consider minimizing the square error between the autoregressive model and the predicted value y^ k y k The least squares method is used to approximate. The following formula 2 is a conditional formula for minimizing the squared error between the time series data and the predicted value by the autoregressive model.

[0013]

number

[0014] From formula 2, the relationship of formula 3 below is satisfied.

[0015]

number

[0016] Moreover, by transforming equation 3 (in matrix notation), we obtain the following equation 4.

[0017]

number

[0018] R in Equation 4 jl is called the autocorrelation of the time series data y, and is the value defined by the following equation 5. In this case, |jl| is called the time lag.

[0019]

number

[0020] Based on equation 4, consider equation 6, which is a relational equation related to the coefficients of the autoregressive model below. Equation 6 is an equation derived from the condition for minimizing the error between the predicted value of time series data by the autoregressive model and the time series data at the time corresponding to the predicted value, and is called the Yule-Walker equation. Equation 6 is also a linear equation whose variable vector is a vector consisting of the coefficients of the autoregressive model, and the constant vector on the left side of equation 6 is a vector whose components are the autocorrelation of time series data with time lags from 1 to m, hereinafter referred to as the autocorrelation vector. The coefficient matrix on the right side of equation 6 is a matrix whose components are the autocorrelation of time series data with time lags from 0 to m-1, hereinafter referred to as the autocorrelation matrix.

[0021]

number

[0022] In addition, the autocorrelation matrix on the right side of Equation 6 (R jl The m×m matrix composed of the above is expressed as the autocorrelation matrix R as shown in the following equation 7.

[0023]

number

[0024] Then, using some of the eigenvalues ​​of the autocorrelation matrix R, the autocorrelation matrix R is rewritten so that the effect of noise contained in the time-series data y is reduced and the signal component is emphasized (the S / N ratio is increased). First, singular value decomposition is performed on the autocorrelation matrix R. Since the elements of the autocorrelation matrix R are symmetric, singular value decomposition of the autocorrelation matrix R results in a product of an orthogonal matrix U, a diagonal matrix Σ, and a transpose of the orthogonal matrix U, as shown in the following formula 8.

[0025]

number

[0026] The matrix Σ in Equation 8 is a diagonal matrix whose diagonal elements are eigenvalues ​​of the autocorrelation matrix R, as shown in Equation 9. The diagonal elements of the diagonal matrix Σ are expressed as σ 11 , σ 22 , , σ mm The matrix U is an orthogonal matrix in which each column component vector is an eigenvector of the autocorrelation matrix R. The column component vectors of the orthogonal matrix U are defined as u 1 , u 2 , , u m Let u be the eigenvector of the autocorrelation matrix R. j The eigenvalue for σ jj The eigenvalues ​​of the autocorrelation matrix R are variables that reflect the sum of the intensities of the frequency components contained in the time waveform of the predicted value of the time series data by the autoregressive model.

[0027]

number

[0028] σ is the diagonal element of the diagonal matrix Σ obtained by singular value decomposition of the autocorrelation matrix R. 11 , σ 22 , , σ mm The values ​​are in descending order to simplify the notation of the formula. Matrix R' is defined as shown in the following formula 10 by using s eigenvalues ​​to be used, which is a set number that is 1 or more and less than m, from the largest eigenvalue among these eigenvalues ​​of autocorrelation matrix R. Matrix R' is a matrix obtained by approximating autocorrelation matrix R using s eigenvalues ​​to be used among the eigenvalues ​​of autocorrelation matrix R.

[0029]

number

[0030] Matrix U in Equation 10 s is an m × s matrix composed of s column component vectors (eigenvectors corresponding to the eigenvalues ​​used) from the left of the orthogonal matrix U in Equation 8. That is, the matrix U s is a submatrix formed by cutting out the left m×s elements from the orthogonal matrix U. Also, Us T U s is the transpose of the matrix U in Eq. T The matrix Σ in Equation 10 is an s × m matrix consisting of s row component vectors from the top. s is an s × s matrix consisting of s columns from the left and s rows from the top of the diagonal matrix Σ in Equation 8. In other words, the matrix Σ s is a submatrix formed by cutting out the upper left s × s elements from the diagonal matrix Σ. matrix Σ s and matrix U s When expressed as a matrix element, it becomes as shown in the following Equation 11.

[0031]

number

[0032] By using matrix R′ instead of autocorrelation matrix R, the relational expression of Equation 6 can be rewritten as Equation 12 below.

[0033]

number

[0034] By transforming Equation 12, we obtain Equation 13 for calculating the coefficient α. Using the coefficient α calculated by Equation 13, the predicted value y^ is calculated by Equation 1. k The model that calculates the above is called the "modified autoregressive model." In the modified autoregressive model, the predicted value y^ is calculated with the influence of noise reduced by using only some of the eigenvalues ​​of the autocorrelation matrix R. k can be sought. So far, the diagonal elements of the diagonal matrix Σ are 11 , σ 22 , , σ mm Although the values ​​of are explained as being in descending order, the diagonal elements of the diagonal matrix Σ do not need to be in descending order in the process of calculating the coefficient α. In that case, sis a submatrix that is constructed by extracting the column component vectors (eigenvectors) corresponding to the eigenvalues ​​used, rather than extracting the left m × s elements from the orthogonal matrix U, and the matrix Σ s is a submatrix that is cut out so that the eigenvalues ​​to be used are the diagonal components, rather than cutting out the upper left s × s elements from the diagonal matrix Σ. Equation 13 is the equation used to determine the coefficients of the modified autoregressive model. s is a third matrix that is a submatrix of an orthogonal matrix obtained by singular value decomposition of the autocorrelation matrix R and has eigenvectors corresponding to the eigenvalues ​​to be used as column component vectors. Also, the matrix Σ s is a submatrix of the diagonal matrix obtained by singular value decomposition of the autocorrelation matrix R, and is a second matrix having the eigenvalues ​​to be used as diagonal elements. s Σ s U s T is the matrix Σ s and matrix U s The first matrix is ​​a matrix derived from

[0035]

number

[0036] The coefficient α of the modified autoregressive model is obtained by calculating the right side of Equation 13. An example of a method for deriving the coefficient of the modified autoregressive model has been described above, and the derivation of the coefficient of the autoregressive model on which it is based has been described using the least squares method for the predicted value for intuitive ease of understanding. However, a method is generally known in which an autoregressive model is defined using the concept of a stochastic process and the coefficient is derived. In that case, the autocorrelation is expressed by the autocorrelation of the stochastic process (population), and the autocorrelation of this stochastic process is expressed as a function of the time difference. Therefore, the autocorrelation of the time series data in this embodiment may be replaced with a value calculated by another calculation formula as long as it approximates the autocorrelation of the stochastic process, for example, R 22 ~R mmare autocorrelations with zero time lag, but these are calculated using R 11 can also be replaced with.

[0037] (experiment) The rolling direction force acting on the chocks of the work rolls of a rolling mill used in rolling a metal plate (hereinafter referred to as the rolling direction force) is a physical quantity that is not measured unless a load in the rolling direction is applied to the corresponding chock. A chock is a mechanism that includes a bearing that supports the rolls of the rolling mill and a mechanism that holds the bearing. Therefore, the inventors considered that the rolling direction force is a physical quantity that is less likely to generate noise compared to sound and vibration. Therefore, the inventors came up with the idea that it may be possible to diagnose an abnormality in the spindle connected to the work rolls of the rolling mill based on the coefficients of a modified autoregressive model that predicts the rolling direction force acting on the chocks of the work rolls of the rolling mill when rolling a metal plate using the rolling mill. The inventors conducted an experiment to verify the effectiveness of the obtained idea. The details of this experiment are described below.

[0038] First, the rolling mill used in this experiment (hereinafter, the rolling mill used) will be described with reference to Figs. Fig. 1 shows the mechanism around the work rolls of the rolling mill in use as viewed from the work side (the direction indicated by the arrow 210 in Fig. 2). The drive side is the side of the work rolls in the direction of the rotation axis on which a motor used to rotate the work rolls is located. The work side is the side of the work rolls in the direction of the rotation axis opposite the drive side. 2 shows a cross section of the mechanism shown in FIG. 1 taken along a plane 110 shown in FIG.

[0039] Each of the rolls 100 and 105 is a work roll in the rolling mill used. A work roll is a roll that directly rolls a metal plate. That is, the rolls 100 and 105 rotate while sandwiching the metal plate, thereby working together to roll the metal plate. In addition, both ends of the rolls 100 and 105 in the direction of the rotation axis have a smaller diameter than the portion that directly rolls the metal plate, and are supported by chocks. The spindle 202 is a mechanism for transmitting torque to the roll 100, and is connected to an end of the roll 100 on the drive side via a joint. The roll 100 rotates by the torque transmitted from the spindle 202. The spindle 204 is a mechanism for transmitting torque to the roll 105, and is connected to an end of the roll 105 on the drive side via a joint. The roll 105 rotates by the torque transmitted from the spindle 204. The motor 201 is a motor for rotating the spindle 202, and rotates the roll 100 by rotating the spindle 202. The motor 203 is a motor for rotating the spindle 204, and rotates the roll 105 by rotating the spindle 204. The chock 101W is a chock that supports the end of the roll 100 on the work side in the rotational axis direction. The chock 101D is a chock that supports the end of the roll 100 on the drive side in the rotational axis direction. The chock 106W is a chock that supports the end of the roll 105 on the work side in the rotational axis direction. The chock 106D is a chock that supports the end of the roll 105 on the drive side in the rotational axis direction.

[0040] Load detection devices 102W and 103W are arranged at both ends of the chock 101W in the rolling direction (the exit side and the entry side of the metal plate). Load detection devices 102D and 103D are arranged at both ends of the chock 101D in the rolling direction. Load detection devices 107W and 108W are arranged at both ends of the chock 106W in the rolling direction (the exit side and the entry side of the metal plate). Load detection devices 107D and 108D are arranged at both ends of the chock 106D in the rolling direction. Each of the load detection devices 102W and 103W is sandwiched between the chock 101W and a fixed part of the rolling mill, and detects a load in the rolling direction related to the chock 101W. Each of the load detection devices 102D and 103D is sandwiched between the chock 101D and a fixed part of the rolling mill, and detects a load in the rolling direction related to the chock 101D. Each of the load detection devices 107W and 108W is sandwiched between the chock 106W and a fixed part of the rolling mill, and detects a load in the rolling direction related to the chock 106W. Each of the load detection devices 107D and 108D is sandwiched between the chock 106D and a fixed part of the rolling mill, and detects a load in the rolling direction related to the chock 106D.

[0041] The measuring device 104W is a measuring device that measures the rolling direction force acting on the chock 101W from the load in the rolling direction acting on the chock 101W detected by the load detection device 102W and the load detection device 103W. The measuring device 104D is a measuring device that measures the rolling direction force acting on the chock 101D from the load in the rolling direction acting on the chock 101D detected by the load detection device 102D and the load detection device 103D. The measuring device 109W is a measuring device that measures the rolling direction force acting on the chock 106W from the load in the rolling direction acting on the chock 106W detected by the load detection device 107W and the load detection device 108W. The measuring device 109D is a measuring device that measures the rolling direction force acting on the chock 106D from the load in the rolling direction acting on the chock 106D detected by the load detection device 107D and the load detection device 108D. In addition, in FIG. 1, which shows the situation as seen from the work side, chock 101D, load detection device 102D, load detection device 103D, measuring device 104D, chock 106D, load detection device 107D, load detection device 108D, and measuring device 109D are not shown.

[0042] The inventors performed the following operations using a spindle (hereinafter referred to as a deteriorated spindle) in a deteriorated state (a state at a point in time a set period before the point in time when breakage is predicted) as the spindle 204. In this experiment, the spindle 202 is a spindle (hereinafter referred to as a normal spindle) in a normal state (a state without abnormalities and without deterioration due to age). The inventors measured the rolling direction forces of the chocks 101W, 101D, 106W, and 106D periodically at a period of 26 [ms (milliseconds)] using the measuring devices 104W, 104D, 109W, and 109D, respectively, during rolling of a metal plate using a rolling mill in which the spindle 204 is a deteriorated spindle. As a result, the inventors obtained measurement data of the rolling direction forces periodically measured for each of the chocks 101W, 101D, 106W, and 106D. Hereinafter, the measurement data measured using the measuring device 109D is referred to as the first measurement data. Hereinafter, the measurement data measured using the measuring device 109W is referred to as the second measurement data. Hereinafter, the measurement data measured using the measuring device 104D is referred to as the third measurement data. Hereinafter, the measurement data measured using the measuring device 104W is referred to as the fourth measurement data.

[0043] The inventors defined the second measurement data, which is time-series data, as y, generated an autocorrelation matrix R using Equation 5 and Equation 7, and performed singular value decomposition on the generated R. In this experiment, the value of m was set to 100, and the value of M was set to 2000. That is, each of the first to fourth measurement data includes M or more pieces of data, and the rolling direction force is measured M or more times. Fig. 3 is a diagram showing an example of a distribution of eigenvalues ​​obtained by singular value decomposition of the autocorrelation matrix R generated using Equation 5 and Equation 7, with the second measurement data being y. The horizontal axis of the graph in Fig. 3 indicates the index of the eigenvalue. The vertical axis of the graph in Fig. 3 indicates the value of the eigenvalue. The inventors checked the graph in Fig. 3 and noticed that there was one eigenvalue that was significantly higher than the other eigenvalues. Therefore, in this experiment, the inventors set the number of eigenvalues ​​(s) used in the modified autoregressive model to 1.

[0044] Then, the inventors determined a modified autoregressive model for reproducing the data of the force in the rolling direction applied to the corresponding chock for each of the four acquired measurement data (first to fourth measurement data) in the following manner. That is, the inventors defined the measurement data, which is time-series data, as y, and generated an autocorrelation matrix R using Equation 5 and Equation 7. Then, the inventors subjected the generated R to singular value decomposition, and used s(1) eigenvalues ​​among the obtained eigenvalues ​​to calculate the coefficients (α 1 ~α m ) was obtained. By substituting the coefficients obtained here into Equation 1, a modified autoregressive model for obtaining a predicted value of the rolling direction force from the actual value of the rolling direction force is obtained. In the following, we use the coefficients (α 1 ~α m ) is the first coefficient. In the following, the coefficient of the modified autoregressive model obtained from the second measurement data (α 1 ~α m ) is the second coefficient. In the following, the coefficient of the modified autoregressive model obtained from the third measurement data (α 1 ~α m ) is the third coefficient. In the following, the coefficient of the modified autoregressive model obtained from the fourth measurement data (α 1 ~α m ) is the fourth coefficient. After the inventors determined the first to fourth coefficients, the rolling mill continued to operate, and the inventors confirmed that the spindle 204 had broken.

[0045] The inventors also carried out the same operation using a normal spindle as the spindle 204. That is, the inventors periodically measured the rolling direction forces related to the chocks 101W, 101D, 106W, and 106D at a period of 26 [ms (milliseconds)] using the measuring devices 104W, 104D, 109W, and 109D, respectively, during rolling of a metal plate using a rolling mill in which the spindle 204 is a normal spindle. As a result, the inventors obtained measurement data of the rolling direction forces periodically measured for each of the chocks 101W, 101D, 106W, and 106D. Hereinafter, the measurement data measured using the measuring device 109D is referred to as the fifth measurement data. Hereinafter, the measurement data measured using the measuring device 109W is referred to as the sixth measurement data. Hereinafter, the measurement data measured using the measuring device 104D is referred to as the seventh measurement data. Hereinafter, the measurement data measured using the measuring device 104W is referred to as the eighth measurement data.

[0046] Then, the inventors determined a modified autoregressive model for reproducing the data of the force in the rolling direction applied to the corresponding chock for each of the acquired four pieces of measurement data (the fifth to eighth measurement data) in the following manner. That is, the inventors defined the measurement data, which is time-series data, as y, and generated an autocorrelation matrix R using Equation 5 and Equation 7. Then, the inventors subjected the generated R to singular value decomposition, and used s(1) eigenvalues ​​among the obtained eigenvalues ​​to calculate the coefficients (α 1 ~α m ) was obtained. By substituting the coefficients obtained here into Equation 1, a modified autoregressive model for obtaining a predicted value of the rolling direction force from the actual value of the rolling direction force is obtained. Below, we use the coefficients (α 1 ~α m ) is the fifth coefficient. In the following, the coefficient of the modified autoregressive model obtained from the sixth measurement data (α 1 ~α m ) is the sixth coefficient. In the following, the coefficient of the modified autoregressive model obtained from the seventh measurement data (α 1 ~α m) is the seventh coefficient. In the following, the coefficient of the modified autoregressive model obtained from the eighth measurement data (α 1 ~α m ) is the eighth coefficient.

[0047] The first to eighth coefficients will be described with reference to FIG. 4 and FIG. Each graph in FIG. 4 is a graph showing a pattern of coefficients (first to fourth coefficients) of a modified autoregressive model obtained from measurement data of rolling direction forces for each chock of a rolling mill in which the spindle 204 is a deteriorated spindle. The pattern of coefficients of a modified autoregressive model is information showing the shape when the components of these coefficients are arranged. Each graph in FIG. 5 is a graph showing a pattern of coefficients (fifth to eighth coefficients) of a modified autoregressive model obtained from measurement data of rolling direction forces for each chock of a rolling mill in which the spindle 204 is a normal spindle. The horizontal axis of each graph in FIG. 4 and FIG. 5 indicates the index of the coefficients. Moreover, the vertical axis of each graph in FIG. 4 and FIG. 5 indicates the value of the coefficients.

[0048] The graph in Fig. 4(a) shows the pattern of the first coefficient. The graph in Fig. 4(b) shows the pattern of the second coefficient. The graph in Fig. 4(c) shows the pattern of the third coefficient. The graph in Fig. 4(d) shows the pattern of the fourth coefficient. The graph in Fig. 5(a) shows the pattern of the 5th coefficient. The graph in Fig. 5(b) shows the pattern of the 6th coefficient. The graph in Fig. 5(c) shows the pattern of the 7th coefficient. The graph in Fig. 5(d) shows the pattern of the 8th coefficient.

[0049] The graphs of Fig. 4(a) and Fig. 5(a) both show the pattern of the coefficients of the modified autoregressive model obtained from the measurement data of the rolling direction force for the chock 106D. The graphs of Fig. 4(b) and Fig. 5(b) both show the pattern of the coefficients of the modified autoregressive model obtained from the measurement data of the rolling direction force for the chock 106W. The graphs of Fig. 4(c) and Fig. 5(c) both show the pattern of the coefficients of the modified autoregressive model obtained from the measurement data of the rolling direction force for the chock 101D. The graphs of Fig. 4(d) and Fig. 5(d) both show the pattern of the coefficients of the modified autoregressive model obtained from the measurement data of the rolling direction force for the chock 101W.

[0050] The inventors compared the graphs of Figures 4(b) and 5(b) and noticed that the graph of Figure 4(b) shows a waveform that is significantly more fluctuating than the graph of Figure 5(b). The inventors also compared the graphs of Figures 4(a) and 5(a) and noticed that the graph of Figure 4(a) shows a waveform that is more fluctuating than the graph of Figure 5(a), although not as much as the difference between the graphs of Figures 4(b) and 5(b). The inventors also compared the graphs of Figures 4(c) and 5(c) and noticed that the graph of Figure 4(c) shows a waveform that is more fluctuating than the graph of Figure 5(c), although not as much as the difference between the graphs of Figures 4(b) and 5(b). The inventors compared the graphs of FIG. 4(d) and FIG. 5(d) and noticed that the graph of FIG. 4(d) exhibited a waveform that fluctuated compared to the graph of FIG. 5(d), although not as much as the difference between the graphs of FIG. 4(b) and FIG. 5(b).

[0051] The inventors confirmed that the second coefficient calculated from the rolling direction force on the chock 106W on the work side of the roll 105 rotated by the deteriorated spindle shows a waveform that fluctuates significantly compared to the sixth coefficient. As a result, the inventors confirmed that the pattern of the coefficients of the corrected autoregressive model calculated from the measurement data of the rolling direction force applied to the chock 106W indicates an abnormality in the spindle 204. The inventors also inferred that the reason why the difference between the first coefficient and the fifth coefficient calculated from the rolling direction force on the chock 106D on the drive side of the roll 105 rotated by the deteriorated spindle is not as large as the difference between the second coefficient and the sixth coefficient is because the spindle 204 restricts the movement of the chock 106D in the rolling direction. The inventors also considered that the fluctuations in the coefficients found in the rolling direction for the other chocks represented the backlash of the equipment caused by the use of the equipment before and after the replacement of the spindle.

[0052] In this experiment, although not shown in FIG. 1, load detection devices are provided at the upper and lower ends of the chock 106D. In addition, a measuring device (hereinafter referred to as a first gravity direction force measuring device) that measures a force in the gravity direction acting on the chock 106D from the load detected by the load detection devices is connected to these load detection devices. Similarly, a load detection device is provided at the upper and lower ends of the chock 106W. In addition, a measuring device (hereinafter referred to as a second gravity direction force measuring device) that measures a force in the gravity direction acting on the chock 106W from the load detected by the load detection devices is connected to these load detection devices.

[0053] When the inventors obtained the first to fourth measurement data using a deteriorated spindle as the spindle 204, they further measured the gravity direction forces on the chocks 106D and 106W periodically at a period of 26 ms using the first gravity direction measurement device and the second gravity direction measurement device. Hereinafter, the measurement data measured using the first gravity direction measurement device will be referred to as the ninth measurement data. Also, below, the measurement data measured using the second gravity direction measurement device will be referred to as the tenth measurement data. Furthermore, when the inventors obtained the fifth to eighth measurement data using a normal spindle as the spindle 204, they further measured the gravity direction forces on the chocks 106D and 106W periodically at a cycle of 26 [ms] using the first gravity direction measurement device and the second gravity direction measurement device. Hereinafter, the measurement data measured using the first gravity direction measurement device will be referred to as the eleventh measurement data. Also, below, the measurement data measured using the second gravity direction measurement device will be referred to as the twelfth measurement data.

[0054] The inventors determined a modified autoregressive model for reproducing the data of the force in the rolling direction applied to the corresponding chock for each of the four pieces of measurement data, the ninth measurement data to the twelfth measurement data, in the following manner. That is, the inventors defined the measurement data, which is time-series data, as y, and generated an autocorrelation matrix R using Equation 5 and Equation 7. Then, the inventors subjected the generated R to singular value decomposition, and used s(1) eigenvalues ​​among the obtained eigenvalues ​​to calculate the coefficients (α 1 ~α m ) was sought. Below, we use the coefficients (α 1 ~α m ) is the 9th coefficient. In the following, the coefficient of the modified autoregressive model obtained from the 10th measurement data (α 1 ~α m ) is the 10th coefficient. In the following, the coefficient of the corrected autoregressive model obtained from the 11th measurement data (α 1 ~α m) is the 11th coefficient. In the following, the coefficient of the corrected autoregressive model obtained from the 12th measurement data (α 1 ~α m ) is the 12th coefficient.

[0055] Each graph in Fig. 6 shows a pattern for each of the 9th to 12th coefficients. The horizontal axis of each graph in Fig. 6 indicates the index of the coefficient. Furthermore, the vertical axis of each graph in Fig. 6 indicates the value of the coefficient. The graph in Figure 6(a) shows the pattern of the 9th coefficient. The graph in Figure 6(b) shows the pattern of the 10th coefficient. The graph in Figure 6(c) shows the pattern of the 11th coefficient. The graph in Figure 6(d) shows the pattern of the 12th coefficient. The graphs in Figures 6(a) and 6(c) show the coefficient patterns of the modified autoregressive model obtained from the measurement data of the gravity-direction force for the chock 106D. The graphs in Figures 6(b) and 6(d) show the coefficient patterns of the modified autoregressive model obtained from the measurement data of the gravity-direction force for the chock 106W.

[0056] The inventors confirmed that there is no significant difference between Figure 6(a) and Figure 6(c) and also confirmed that there is no significant difference between Figure 6(b) and Figure 6(d). For this reason, the inventors confirmed that the pattern of coefficients of the modified autoregressive model obtained from the measurement data of the gravity-direction force on the chocks did not indicate any abnormality in the spindle.

[0057] The inventors confirmed that the pattern of coefficients of a modified autoregressive model obtained from measurement data of the rolling direction force on the chock indicates spindle abnormality, and came up with a method for diagnosing spindle abnormalities (hereinafter referred to as the idea method). The concept behind this method is outlined below. When a rolling mill with a normal work roll spindle is used to roll a metal plate, measurement data of the rolling direction force for the chock supporting the work roll is acquired. Then, from each of the acquired measurement data, a non-negative matrix indicating the coefficient α of the modified autoregressive model is identified as a teacher basis matrix. Then, the coefficient α of the modified autoregressive model is obtained from the measurement data of the rolling direction force for the chock of the rolling mill in which the state of the spindle connected to the work roll is unknown, and a matrix storing non-negative data indicating the obtained coefficient α is subjected to non-negative matrix factorization into a teacher basis matrix, a weight matrix of the teacher basis, an extracted basis matrix indicating the basis extracted from this matrix, and a weight matrix of the extracted basis. Then, based on the comparison result between the weight matrix of the teacher basis and the weight matrix of the extracted basis and the comparison result between the extracted basis matrix and the teacher basis matrix, it is diagnosed whether the state of the spindle is a state corresponding to the teacher basis matrix (normal state) or not. This is the outline of the concept method.

[0058] Therefore, the inventors conducted the following experiment to verify the effectiveness of the ideation method. The inventors performed the following operations by sequentially using the chocks 106D, 106W, 101D, and 101W as chocks to be measured for rolling direction force (hereinafter, referred to as measurement target chocks). By using the non-negative matrix factorization described in WO 2019 / 026980, the inventors determined an m(100) × 1 matrix that stores data indicating the pattern of coefficients corresponding to the chock to be measured among the fifth to eighth coefficients as the teacher basis matrix F, which is a matrix indicating coefficients corresponding to a normal state.

[0059] In addition, the inventors performed q' times of periodically measuring the rolling direction force of the measurement target chock at least M times at a period of 26 [ms] while the rolling mill in which the spindle 202 is a normal spindle and the spindle 204 is a deteriorated spindle was rolling a metal plate. In this experiment, q' is 1. As a result, the inventors obtained q' pieces of measurement data. Then, for each of the q' pieces of acquired measurement data, the inventors defined the measurement data as y and generated an autocorrelation matrix R using Equation 5 and Equation 7. Then, the inventors subjected the generated R to singular value decomposition, and calculated the coefficients (α 1 ~α m ) was calculated. The inventors then used the following Equation 14 to calculate the data matrix Y d It was established.

[0060]

number

[0061] The data in each column of the matrix in Equation 14 indicates the coefficients α of the obtained q' corrected autoregressive models. That is, α i , j indicates the i-th element of the j-th coefficient α of the q' modified autoregressive model coefficients α. In this experiment, q' is 1, so Y d The coefficients of the corrected autoregressive model (α 1 ~α m ) are α 1 , 1 ~α m , 1 It will be stored as. In this experiment, the data matrix Y d Decompose the data matrix Y into multiple matrices with non-negative values. d To decompose into multiple non-negative matrices, d Without changing the pattern of the coefficients α in each column of d Each component of the matrix Y d The minimum value of the elements of the data matrix Y d By subtracting each element of d The adjusted data matrix Y dEach column of the above table stores non-negative data indicating the pattern of the coefficient α in the modified autoregressive model. The inventors calculate the adjusted data matrix Y d into multiple non-negative matrices. More specifically, the inventors decomposed Y d Let F be the teacher basis matrix, G be the teacher weight matrix that indicates the weights for the teacher basis, and Y be the data matrix, which are non-negative matrices. d The matrix Q indicates the extraction basis, which is the basis extracted from the matrix Y. The matrix W indicates the weights for the extraction basis. d The process of decomposing Y into F, G, Q, and W can be considered as the following process. d This can be regarded as a process of decomposing the data of the coefficient α stored in each column into a weighted sum of the pattern indicated by the teacher base and other patterns. In this experiment, F is a matrix of size m(100)×1, and G is a matrix of size 1×q′(1) (scalar value in this experiment). Q is a matrix of size m(100)×(number n (set to 1 in this experiment) indicating the number of bases extracted from the data matrix). W is a matrix of size n(1)×q′(1) (scalar value in this experiment). In the following description, the teacher basis matrix F is also referred to as the teacher basis vector F, and the teacher weight matrix G is also referred to as the weight coefficient G. When n is 1, the extracted basis matrix Q is also referred to as the extracted basis vector Q, and the extracted weight matrix W is also referred to as the weight coefficient W. The value of the jth column element in G is the adjusted data matrix Y d The value of the element in the i-th row and j-th column of W indicates the weight of the teacher basis component contained in the data indicating the pattern of the coefficient α stored in the j-th column of d This indicates the weight of the component of the extraction basis stored in the i-th column of Q contained in the data indicating the pattern of the coefficient α stored in the j-th column of Q.

[0062]

number

[0063] Y d Here, we explain how to decompose into F, G, Q, and W as in Equation 15. The cost function J d Define.

[0064]

number

[0065] The Fr in the first term on the right side of Equation 16 is a subscript indicating that it is a Frobenius norm. In other words, the first term on the right side of Equation 16 is a Frobenius norm. The first term on the right side of Equation 16 is the sum of the product of F and G and the product of Q and W, and Y d The second term on the right side of Equation 16 indicates the sparsity constraint of the teacher weight matrix. 1 is a predetermined real number. k and t in the second term on the right side of Equation 16 are indices indicating the row and column of the matrix, respectively. The third term on the right side of Equation 16 indicates the sparsity constraint of the extraction weight matrix. 2 is a predetermined real number. The l and t in the third term on the right side of Equation 16 are indices indicating the row and column of the matrix, respectively. The fourth term on the right side of Equation 16 is a term indicating the orthonormal constraint of the extraction basis (i.e., the constraint that the entire set of patterns stored in each column of the extraction basis matrix Q approximately forms an orthonormal system). ε in the fourth term on the right side of Equation 16 1 is a predetermined real number. i and i' in the fourth term on the right side of Equation 16 are indexes indicating the row and column of the matrix, respectively. I in the fourth term on the right side of Equation 16 is a unit matrix. The fifth term on the right side of Equation 16 is a term indicating an orthogonal constraint between the teacher basis and the extracted basis (i.e., a constraint that the teacher basis matrix F and all patterns stored in each column of the extracted basis matrix Q are approximately orthogonal). ε in the fifth term on the right side of Equation 16 2 is a predetermined real number. In the fourth term on the right side of Equation 16, i and i' are indexes indicating the row and column of the matrix, respectively. In this experiment, we do not add any of the following constraints: sparseness constraint of the teacher weight matrix, sparseness constraint of the extraction weight matrix, orthonormal constraint of the extraction basis, or orthogonal constraint between the teacher basis and the extraction basis. 1 , δ 2 , ε 1 , ε 2 Each of them is set to 0. Therefore, the cost function J d is the first term on the right hand side of Equation 16 alone. J d By updating the values ​​of G, Q, and W, the value of Y d is decomposed into F, G, Q, and W. The cost function J defined in the following Equation 17 is d This involves solving the minimization problem of

[0066]

number

[0067] In this experiment, the inventors used the cost function J d In order to minimize this, we performed the following operations. That is, by repeatedly updating G, Q, and W, we minimize the cost function J d In addition, the cost function J d In order to minimize , a method other than the method described below (for example, an optimization method such as Newton's method or stochastic gradient descent) may be used. We will now explain the update of G. In this experiment, G was updated as shown in the following formula 18.

[0068]

number

[0069] In Equation 18, k and t are indices that indicate the rows and columns of the matrix, respectively. G kt is a non-negative value indicating the update step size for the k,t element of G. Cost function J d By partially differentiating with respect to G, we obtain the following Equation 19.

[0070]

number

[0071] E in Equation 19 3 is a matrix of size 1×q' with all elements being 1. The inventors obtained the following Equation 20, which indicates G after the update, by substituting Equation 19 into Equation 18.

[0072]

number

[0073] Since matrix G is a non-negative value, the value of equation 20 must be a non-negative value. The last term on the rightmost side of equation 20 is always a non-negative term. In other words, if the value of the equation obtained by excluding the last term from the rightmost side of equation 20 is 0, then G after the update will always be a non-negative value. For this reason, the inventors updated matrix G as shown in the following equation 21 so as to satisfy the condition that the equation obtained by excluding the last term from the rightmost side of equation 21 is 0.

[0074]

number

[0075] From Equation 21, η G kt is expressed as follows:

[0076]

number

[0077] The inventors obtained the following formula 23, which indicates G after the update, by substituting formulas 19 and 22 into formula 18.

[0078]

number

[0079] That is, the inventors d , F, G, Q, and W before updating at the time of processing, and a predetermined coefficient δ 1 (In this experiment, 0) and,G was updated using Equation 23 based on. Next, we will explain how to update Q. In this experiment, Q was updated as shown in the following Equation 24.

[0080]

number

[0081] In Equation 24, w and t are indices indicating the rows and columns of the matrix, respectively. Q wt is a non-negative value indicating the update step size for the w,t element of Q. Cost function J d By partially differentiating with respect to Q, we obtain the following equation 25.

[0082]

number

[0083] E in Equation 25 4 is a matrix of size n × n with all elements being 1. 5 is a matrix of size 1×1 with all elements being ones. By substituting Equation 25 into Equation 24, we obtain the following Equation 26, which shows the updated Q.

[0084]

number

[0085] Since the matrix Q is a non-negative value, the value of Equation 26 must be a non-negative value. The last term on the rightmost side of Equation 26 is always a non-negative term. In other words, if the value of the equation obtained by excluding the last term from the rightmost side of Equation 26 is 0, then Q after the update will always be a non-negative value. Therefore, the inventors updated the matrix Q as shown in Equation 27 below, so as to satisfy the condition that the equation obtained by excluding the last term from the rightmost side of Equation 26 is 0.

[0086]

number

[0087] From Equation 27, η Q wt is expressed as follows:

[0088]

number

[0089] The inventors obtained the following Equation 29, which indicates G after the update, by substituting Equation 25 and Equation 28 into Equation 24.

[0090]

number

[0091] That is, Y d , F, G, Q, and W before the update at the time of processing, and a predetermined coefficient ε 1 , ε 2 (In this experiment, both are 0) and, based on this, Q was updated using Equation 29. Next, we will explain the update of W. In this experiment, the inventors updated W as shown in the following formula 30.

[0092]

number

[0093] In Equation 30, l and t are indices indicating the rows and columns of the matrix, respectively. W lt is a non-negative value indicating the update step size for the l,t element of W. The inventors define a cost function J d By partially differentiating with respect to W, we obtain the following equation 31.

[0094]

number

[0095] E6 in Equation 31 is a matrix of size 1×q′ in which all components are 1. By substituting Equation 31 into Equation 30, we obtain the following Equation 32, which shows the updated W.

[0096]

number

[0097] Since the matrix W is a non-negative value, the value of Equation 32 must be a non-negative value. The last term on the rightmost side of Equation 32 is always a non-negative term. In other words, if the value of the equation obtained by excluding the last term from the rightmost side of Equation 32 is 0, then W after updating will always be a non-negative value. Therefore, the inventors updated the matrix W as shown in Equation 33 below, so as to satisfy the condition that the equation obtained by excluding the last term from the rightmost side of Equation 32 is 0.

[0098]

number

[0099] From Equation 33, η W lt is expressed as follows:

[0100]

number

[0101] The inventors obtained the following Equation 35, which indicates the updated W, by substituting Equation 31 and Equation 34 into Equation 30.

[0102]

number

[0103] That is, the inventors d , F, G, Q, and W before updating at the time of processing, and a predetermined coefficient δ 2 (In this experiment, 0) and,G was updated using Equation 35 based on. As described above, in this experiment, the inventors repeatedly updated G using formula 23, Q using formula 29, and W using formula 58, and at each update stage, calculated the Frobenius norms of ΔG, ΔQ, and ΔW, which are the differences obtained by subtracting G, Q, and W before the update from G, Q, and W after the update. The inventors then determined that the cost function J is at an update stage where the ratio of the Frobenius norms of ΔG, ΔQ, and ΔW at each update stage to the Frobenius norms of ΔG, ΔQ, and ΔW at the first update stage is equal to or smaller than a predetermined threshold value. d The value of has converged. And, J d When G, Q, and W converge, they are the cost function J d This allows the inventors to minimize Y d is decomposed into F, G, Q, and W, which are non-negative matrices, as shown in Equation 15. In this experiment, the cost function J d However, as another example, the update of G using the formula 23, the update of Q using the formula 29, and the update of W using the formula 35 are repeatedly performed, and the cost function J is obtained before and after the update of G, Q, and W. d If the fluctuation of the value of J is below a predetermined threshold for a predetermined number of consecutive times, the cost function J d It is acceptable to consider that the value of has converged. d When G, Q, and W converge, they are the cost function J d Alternatively, the matrix that minimizes

[0104] If the chock to be measured is chock 106D (F indicates the pattern of the 5th coefficient, Y d The following describes F, G, Q, and W obtained in the case where 0.04×10 indicates the pattern of the first coefficient. The teacher basis vector F and extracted basis vector Q are as shown in FIG. 7(a). The horizontal axis of the graph in FIG. 7(a) indicates the index of the basis vector (coefficient of the modified autoregressive model). The vertical axis of the graph in FIG. 7(a) indicates the value of the basis vector (coefficient of the modified autoregressive model). The solid line pattern in the graph in FIG. 7(a) indicates the pattern of the teacher basis vector F. The dashed line pattern in the graph in FIG. 7(a) indicates the pattern of the extracted basis vector Q. G is 0.04×10 -4 In addition, W is 0.68×10 -4 It became. Since the weighting coefficient W of the extracted basis vector Q is 10 times larger than the weighting coefficient G of the teacher basis vector F, the inventors noticed that the first coefficient shows a pattern closer to the extracted basis vector Q than to the teacher basis vector F. In addition, the inventors calculated the distance between the teacher basis vector F and the extracted basis vector Q as Σ (i=1) m |F(i)-Q(i)| (the sum of the absolute values ​​of the differences between elements with the same index in F and Q, i.e., L 1 The distance between the two points is defined as the square root of the distance, and the result is 0.770.

[0105] If the chock to be measured is chock 106W (F indicates the pattern of the 6th coefficient, Y d The following describes F, G, Q, and W obtained in the case where 0.72×10 indicates the pattern of the second coefficient. The teacher basis vector F and extracted basis vector Q are as shown in FIG. 7(b). The horizontal axis of the graph in FIG. 7(b) indicates the index of the basis vector (coefficient of the modified autoregressive model). The vertical axis of the graph in FIG. 7(b) indicates the value of the basis vector (coefficient of the modified autoregressive model). The solid line pattern in the graph in FIG. 7(b) indicates the pattern of the teacher basis vector F. The dashed line pattern in the graph in FIG. 7(b) indicates the pattern of the extracted basis vector Q. G is 0.72×10-4 In addition, W is 1.37×10 -4 It became. Since the weighting coefficient W of the extracted basis vector Q is about twice as large as the weighting coefficient G of the teacher basis vector F, the inventors noticed that the second coefficient shows a pattern closer to the extracted basis vector Q than to the teacher basis vector F. In addition, the inventors noticed that the distance (Σ (i=1) m When we calculate |F(i)-Q(i)|, the result is 2.20.

[0106] If the chock to be measured is chock 101D (F indicates the pattern of the 7th coefficient, Y d The following describes F, G, Q, and W obtained in the case where 1.21×10 -4 In addition, W is 0.42×10 -4 It became. Since the weighting coefficient W of the extracted basis vector Q is approximately 1 / 3 of the weighting coefficient G of the teacher basis vector F, the inventors noticed that the third coefficient shows a pattern closer to the teacher basis vector F than to the extracted basis vector Q.

[0107] If the chock to be measured is chock 101W (F indicates the pattern of the 8th coefficient, Y dThe following describes F, G, Q, and W obtained in the case where 2.22×10 -4 In addition, W is 0.83×10 -4 It became. Since the weighting coefficient W of the extracted basis vector Q is approximately 1 / 3 of the weighting coefficient G of the teacher basis vector F, the inventors noticed that the fourth coefficient shows a pattern closer to the teacher basis vector F than to the extracted basis vector Q.

[0108] As shown in Fig. 4(b), the data related to the chock 106W on the work side clearly indicates an abnormality in the spindle 204. Therefore, the inventors considered that F, G, Q, and W obtained when the chock to be measured is 106W contain information indicating an abnormality. The inventors compared F, G, Q, and W obtained when the chock to be measured is chock 106W with F, G, Q, and W obtained when the chock to be measured is another chock, and obtained the following findings. That is, the inventors obtained the findings that when W is significantly higher than G and the distance between F and Q is significantly large, an abnormality occurs in the spindle connected to the roll supported by the chock to be measured. Therefore, the processing of this embodiment is as follows. That is, when a rolling mill with a work roll spindle in a normal state is rolling a metal plate, non-negative data indicating the coefficient α of the modified autoregressive model is obtained as a teacher basis vector from the measurement data of the rolling direction force applied to the chock supporting the work side of the work roll of the rolling mill. Then, when a rolling mill with an unknown spindle state is rolling a metal plate, a data matrix Y d Generate the data matrix Y d is decomposed into a teacher basis vector, a teacher weighting coefficient indicating the weight of the teacher basis vector, an extracted basis vector, and an extracted weighting coefficient indicating the weight of the extracted basis vector. Then, the data matrix Y d This is a process of diagnosing whether the state of the spindle connected to the work roll supported by this chock is normal or not, based on the comparison results between the teacher weighting coefficients obtained by the decomposition and the extracted weighting coefficients, and the comparison results between the teacher basis vectors and the extracted basis vectors.

[0109] (Details of information processing device) FIG. 8 is a diagram showing an example of a hardware configuration of the information processing device 800 of this embodiment. The information processing device 800 is an information processing device that diagnoses an abnormality in the spindle of the roll of a rolling mill to be diagnosed (hereinafter, referred to as the target rolling mill). In this embodiment, the information processing device 800 is a personal computer (PC), but may be another information processing device such as a server device, a tablet device, or a computer incorporated in another device. In this embodiment, the information processing device 800 takes the used rolling mill described in FIGS. 1 and 2 as the target rolling mill. However, as another example, the information processing device 800 may take a rolling mill having a different structure from the used rolling mill described in FIGS. 1 and 2 as the target rolling mill. For example, the information processing device 800 may take a rolling mill having a structure in which a spindle connected to upper and lower work rolls via a pinion gear and rotation is transmitted to the upper and lower work rolls by using one motor as the target rolling mill. In addition, in this embodiment, each measuring device that measures the rolling direction force applied to the chocks of the target rolling mill measures the rolling direction force applied to the corresponding chock from the rolling direction load detected by a load detection device arranged on the entry side and exit side of the corresponding chock. However, as another example, each measuring device may measure the rolling direction force acting on the corresponding chock using only the load in the rolling direction detected by a load detection device disposed on the exit side of the rolling mill. In cases where a force always acts on the exit side in the rolling direction during rolling (for example, when the subject rolling mill is a multi-stage rolling mill with four or more stages and the work rolls are offset in the rolling direction relative to the backup rolls, or when the subject rolling mill has a device such as a mill stabilizer that presses the chocks of the work rolls in the rolling direction), each measuring device can more accurately measure the rolling direction force using only the load detected by the load detection device on the exit side of the rolling mill. The information processing device 800 includes a CPU 801, a main storage device 802, an auxiliary storage device 803, a device I / F 804, an input device 805, and an output device 806. The components are connected via a system bus 807 so as to be able to communicate with each other.

[0110] The CPU 801 is a central processing unit that controls the information processing device 800. The main memory device 802 is a memory device such as a RAM (Random Access Memory) that functions as a work area for the CPU 801 and a temporary storage location for data. The auxiliary storage device 803 is a storage device that stores various programs, setting data, data of the rolling direction force output from the measuring device of the rolling direction force, etc. In this embodiment, the auxiliary storage device 803 is an HDD (Hard Disk Drive), but may be another storage device such as a ROM (Read Only Memory) or an SSD (Solid State Drive) as another example. The device I / F 804 is an interface used for exchanging information with an external device such as a measuring device (in this embodiment, measuring devices 104W, 104D, 109W, and 109D) that measures the rolling direction force applied to the chock of the target rolling mill.

[0111] The input device 805 is a device used to input information to the information processing device 800. In this embodiment, the input device 805 is a combination of a mouse and a keyboard. However, as another example, the input device 805 may be another input device such as a touch pad, a touch panel, a controller, or a combination of input devices different from the combination of a mouse and a keyboard. The output device 806 is a device used to output information. In this embodiment, the output device 806 is a monitor, but as another example, it may be another output device such as a display unit of a touch panel. By the CPU 801 executing processing based on a program stored in an auxiliary storage device 803 or the like, functions of the information processing device 800, such as the functions described later in FIG. 9, and processing of the information processing device 800, such as the processing of the flowcharts described later in FIG. 10 and FIG. 11, are realized.

[0112] (Functional configuration of information processing device) An example of functions of the information processing device 800 will be described with reference to FIG. The information processing device 800 includes an acquisition unit 901 , a determination unit 902 , a diagnosis unit 903 , and an output unit 904 . The acquisition unit 901 acquires, via the device I / F 804, measurement data of the rolling direction forces from each of the measuring devices 104W, 104D, 109W, and 109D.

[0113] The determination unit 902 determines the coefficients of a modified autoregressive model that predicts a predicted value of the measurement data acquired by the acquisition unit 901. The modified autoregressive model uses the actual value y of the measurement data y k-1 ~y k-m And the coefficient α for this actual value (=α 1 ~α m ) and, using the predicted value y^ kThe determining unit 902 determines the coefficient α in the modified autoregressive model by using equation 12 (equation 13), which is an equation that uses a first matrix R' (equation 10) obtained by extracting components useful for diagnosing anomalies in an object from the autocorrelation matrix R, instead of the autocorrelation matrix R expressed by equation 7 in equation 6 (Yule-Walker equation) used to determine coefficients in a commonly known autoregressive model. Equation 6 is an equation in which the autocorrelation matrix R, whose components are the autocorrelation of y with time lags from 0 to m-1, is used as a coefficient matrix, and an autocorrelation vector, whose components are the autocorrelation of y with time lags from 1 to m, is used as a constant vector.

[0114] Equation 6 is the predicted value y^ of y calculated by equation 1. k and the predicted value of y^ k The actual value y of y at time k corresponding to k The first matrix R' can be derived as a conditional equation showing a condition for minimizing the square error between the first matrix R and the eigenvalues ​​of the autocorrelation matrix R derived by performing singular value decomposition (equation 8) on the autocorrelation matrix R. The first matrix R' is derived from a diagonal matrix Σ having eigenvalues ​​of the autocorrelation matrix R as diagonal components, and an orthogonal matrix U having eigenvectors of the autocorrelation matrix R as column components. The first matrix R' is derived from a diagonal matrix Σ having eigenvalues ​​of the autocorrelation matrix R as diagonal components, using eigenvalues ​​of the set number of eigenvalues ​​to be used, s, which is equal to or greater than 1 and less than m, of the eigenvalues ​​of the autocorrelation matrix R, as a submatrix of the diagonal matrix Σ, and having eigenvalues ​​of the number of eigenvalues ​​to be used, s, as diagonal components. s and a matrix U which is a submatrix of the orthogonal matrix U and has eigenvectors corresponding to the number s of eigenvalues ​​used as column component vectors. s and the matrix U derived from s Σ s U s T The number of s eigenvalues ​​to be used may be any number that includes the eigenvalue with the largest value among the eigenvalues ​​of the autocorrelation matrix R, and it is preferable that the eigenvalues ​​are selected in descending order of value.

[0115] The diagnosis unit 903 diagnoses whether or not the spindle connected to the work rolls of the rolling mill is in a normal state. In this embodiment, the result of the diagnosis is whether or not the state of the spindle connected to the work rolls of the rolling mill corresponds to the teaching base. The output unit 904 outputs information related to the result of the diagnosis by the diagnosis unit 903 .

[0116] (Teacher basis determination process) The process of determining the teacher basis will be described with reference to FIG. In this embodiment, the information processing device 800 diagnoses an abnormality in the spindle 202. In this embodiment, the chock to be measured for the rolling direction force (measurement target chock) is the chock 101W. The information processing device 800 executes the process of FIG. 10 in advance before executing the diagnosis process described later in FIG. 11. In this embodiment, the value of m is set to 100. The value of M is set to 2000. The value of s is set to 1. In this embodiment, information on each of m, M, and s is stored in advance in the auxiliary storage device 803. The information processing device 800 acquires and uses the information on m, M, and s from the auxiliary storage device 803. In S1001, the acquisition unit 901 acquires measurement data of the rolling direction force applied to the measurement target chock from the measurement device 104W when the target rolling mill in which the spindles 202 and 204 are normal spindles is rolling a metal plate. In this embodiment, the measurement data acquired in S1001 is data of the rolling direction force measured periodically M (2000) times at a period of 26 [ms] by the measurement device 104W. In this embodiment, the acquisition unit 901 acquires the measurement data of the rolling direction force from the measurement device 104W. However, as another example, when the measurement data of the rolling direction force measured by the measurement device 104W is stored in advance in the auxiliary storage device 803, the acquisition unit 901 may acquire this measurement data from the auxiliary storage device 803. In addition, the acquisition unit 901 may acquire the measurement data by accepting transmission of this measurement data from an external device.

[0117] In S1002, the determining unit 902 generates an autocorrelation matrix R for the measurement data acquired in S1001 by setting the measurement data as y and using equations 5 and 7 based on y, m, and M. In S1003, the determination unit 902 performs singular value decomposition on the matrix R obtained in S1002 to obtain the orthogonal matrix U and diagonal matrix Σ of Equation 8, and calculates the eigenvalues ​​σ of the autocorrelation matrix R from the diagonal matrix Σ.11 ~σ mm Get the.

[0118] In S1004, the determination unit 902 determines, for the matrix R obtained in S1002, a plurality of eigenvalues ​​of the matrix R, σ 11 ~σ mm Among them, the largest eigenvalue σ 11 ~σ ss as an eigenvalue of the autocorrelation matrix R to be used for determining the coefficient α of the corrected autoregressive model. In this embodiment, the number of eigenvalues ​​to be used s is set to 1, but may be set to 2 or more. Then, the determining unit 902 determines the selected eigenvalue σ 11 ~σ ss Based on the corresponding measurement data y and the orthogonal matrix U obtained by singular value decomposition of the autocorrelation matrix R, the coefficient α of the modified autoregressive model is determined using Equation 13. Then, the determination unit 902 determines an m×1 matrix storing the coefficient α calculated for the matrix R calculated in S1002 as a teacher basis matrix, and stores information on the teacher basis matrix in the auxiliary storage device 803.

[0119] (Diagnosis Processing) In this embodiment, the information processing device 800 diagnoses the state of the spindle by identifying whether the state of the spindle 202 of the target rolling mill is the normal state indicated by the teacher basis. In this embodiment, the information processing device 800 diagnoses the state of the spindle based on measurement data measured in advance by a rolling direction force measuring device. However, as another example, the information processing device 800 may diagnose the state of the spindle in real time based on measurement data measured by a rolling direction force measuring device. FIG. 11 is a flowchart showing an example of the diagnosis process. The process of diagnosing the spindle 202 by the information processing device 800 will be described with reference to FIG.

[0120] In S1101, the acquisition unit 901 acquires measurement data of the rolling direction force from a measuring device (hereinafter, referred to as the target measuring device) that measures the rolling direction force of the measurement target chock when the target rolling mill, in which the state of each of the spindles 202 and 204 is unknown, is rolling a metal plate. When the measurement target chock is the chock 101W, the target measuring device is the measuring device 104W. In this embodiment, the measurement data acquired in S1101 is data of the rolling direction force measured periodically M (2000) times at a period of 26 [ms] by the target measuring device. In this embodiment, the acquisition unit 901 acquires the measurement data of the rolling direction force from the target measuring device. However, as another example, when the measurement data of the rolling direction force measured by the target measuring device is stored in advance in the auxiliary storage device 803, the acquisition unit 901 may acquire this measurement data from the auxiliary storage device 803. In addition, the acquisition unit 901 may acquire the measurement data by accepting transmission of this measurement data from an external device.

[0121] In S1102, the determining unit 902 generates an autocorrelation matrix R for the measurement data acquired in S1101, with the measurement data being y, based on y, M, and m, using Equations 5 and 7. In S1103, the determination unit 902 performs singular value decomposition on the autocorrelation matrix R generated in S1102 to obtain the orthogonal matrix U and diagonal matrix Σ of Equation 8, and calculates the eigenvalues ​​σ of the autocorrelation matrix R from the diagonal matrix Σ. 11 ~σ mm Get the.

[0122] In S1104, the determination unit 902 determines σ 11 ~σ mm Among them, the largest eigenvalue σ 11 ~σ ss The determining unit 902 selects the measurement data y corresponding to this R and the eigenvalue σ 11 ~σ ssA coefficient α of the modified autoregressive model is determined using Equation 13 based on and an orthogonal matrix U obtained by singular value decomposition of R. The coefficient α determined in S1104 is an example of a modified coefficient, which is a coefficient in the modified autoregressive model determined from the measurement data.

[0123] In S1105, the diagnosis unit 903 acquires, from the auxiliary storage device 803, the teacher basis matrix stored in S1004 (the teacher basis matrix corresponding to the measurement target chock). In S1106, the diagnosis unit 903 sets the coefficient determined in S1104 as α(α 1 ~α m ) as shown in Equation 37, using α, we obtain the data matrix Y d In this embodiment, q′ is set to 1. More specifically, the diagnosis unit 903 generates α 1 ~α m α in Eq. 37 1 , 1 ~α m , 1 By applying d That is, the data matrix Y d Each column of the generated data matrix Y d In this embodiment, the diagnosis unit 903 converts each component of the matrix Y d The minimum value of the elements of the matrix Y d The process of subtracting from each component is performed.

[0124] In S1107, the diagnosis unit 903 generates a matrix F (in this embodiment, a vector) of size m×1 that stores the teacher basis matrix acquired in S1105. Then, the diagnosis unit 903 sets the data of the teacher basis matrix acquired in S1105 to each element of F. In addition, the diagnosis unit 903 sets the data matrix Y d The diagnosis unit 903 also generates a teacher weight matrix G (in this embodiment, a scalar value) of size 1×q′ that stores the weights of the components of the teacher basis included in the data matrix Y dA matrix Q (a vector in this embodiment) of size m×(a predetermined number n) is generated to store the extracted basis matrix, which is a pattern extracted from the data matrix Y d The diagnosis unit 903 extracts the data matrix Y d In this embodiment, an extraction weight matrix W (a scalar value in this embodiment) of size n(1)×q′(1) is generated, which stores the weights of the components of the extraction basis included in Then, the diagnosis unit 903 initializes each of the components G, Q, and W by setting a predetermined initial value for each of the components G, Q, and W.

[0125] In S1108, the diagnosis unit 903 determines whether Y d and F, G, Q, W, and a predetermined coefficient δ 1 , δ 2 , ε 1 , ε 2 Based on this, the cost function J is calculated using Equation 39. d The value of δ is calculated as the cost. 1 , δ 2 , ε 1 , ε 2 Each value is set to 0. The diagnosis unit 903 stores the calculated cost in the main storage device 802 as a pre-update cost. In S1109, the diagnosis unit 903 updates G, Q, and W. More specifically, the diagnosis unit 903 updates Y d , F, G, Q, W before the update, and a predetermined coefficient δ 1 (in this embodiment, 0) and a matrix E 3 , and update G using Equation 46 based on δ. 1 Since is 0, E 3 It is also possible to update G without using

[0126] Also, the diagnosis unit 903 determines whether Y d , F, G, Q, and W before the update, and a predetermined coefficient ε 1 , ε 2(in this embodiment, both are 0) and E 4 and E, a matrix of size 1×1 with all elements being 1. 5 In this embodiment, the diagnosis unit 903 updates Q based on ε 1 , ε 2 Since each is 0, E 4 and E 5 Q may be updated without using Also, the diagnosis unit 903 determines whether Y d , F, G, Q, W before the update, and a predetermined coefficient δ 2 (in this embodiment, 0) and E6, which is a matrix of size 1×q′ with all components being 1, using Equation 58. However, in this embodiment, the diagnosis unit 903 updates W using δ 2 Since is 0, Q may be updated without using E6.

[0127] In S1110, the diagnosis unit 903 determines whether Y d , F, G, Q, W updated in S1109, and coefficient δ 1 , δ 2 , ε 1 , ε 2 Based on this, the cost function J is calculated using Equation 39. d The diagnosis unit 903 calculates the cost by calculating the value of the following equation: The diagnosis unit 903 stores the calculated cost in the main storage device 802 as an updated cost. In S1111, the diagnosis unit 903 determines whether the absolute value of the difference between the post-update cost and the pre-update cost is equal to or less than a predetermined threshold. If the diagnosis unit 903 determines that the absolute value of the difference between the post-update cost and the pre-update cost is equal to or less than the predetermined threshold, the diagnosis unit 903 proceeds to S1112. If the diagnosis unit 903 determines that the absolute value of the difference between the post-update cost and the pre-update cost is greater than the predetermined threshold, the diagnosis unit 903 proceeds to S1113. After the process of S2111, the diagnosis unit 903 stores the post-update cost in the main storage device 802 as a new pre-update cost.

[0128] In S1112, the diagnosis unit 903 adds 1 to the counter value stored in the main memory device 802. Note that the diagnosis unit 903 initializes this counter value to 0 before the start of the processing in FIG. In S1113, the diagnosis unit 903 initializes the counter value stored in the main memory device 802 to 0, and the process proceeds to S2110. In S1114, the diagnosis unit 903 judges whether the counter value stored in the main memory 802 is equal to or greater than a predetermined threshold. When the diagnosis unit 903 judges that the counter value stored in the main memory 802 is equal to or greater than a predetermined threshold, the diagnosis unit 903 calculates the cost function J d It is determined that the value of the counter has converged to a minimum value, and the process proceeds to S1115. If the diagnosis unit 903 determines that the counter value is less than the predetermined threshold value, the process proceeds to S1109.

[0129] In S1115, the diagnosis unit 903 diagnoses whether the state of the spindle 202 connected to the roll 100 supported by the chock to be measured (chock 101W) is normal as indicated by the teacher basis obtained in S1105, based on the comparison result between G and W updated up to the time of processing, and the comparison result between F and Q. In this embodiment, the diagnosis unit 903 identifies the ratio of G to W (in this embodiment, the magnification of W to G (W / G)) as a comparison result between G and W, both of which are scalar values. In addition, the diagnosis unit 903 identifies the distance between F and Q (Σ (i=1) m|F(i)-Q(i)|) is identified. If the value of the comparison result between the identified G and W is equal to or greater than a set threshold (e.g., 2.0, 3.0, etc.) and the value of the comparison result between the identified F and Q is equal to or greater than a set threshold (e.g., 1.0, 2.0, etc.), the diagnosis unit 903 diagnoses that an abnormality has occurred in the spindle connected to the roll supported by the measurement target chock. If the value of the comparison result between the identified G and W is less than the set threshold, or the value of the comparison result between the identified F and Q is less than the set threshold (e.g., 1.0, 2.0, etc.), the diagnosis unit 903 diagnoses that the spindle connected to the roll supported by the measurement target chock is normal. These thresholds may be set according to the management criteria by accumulating data on the ratio of G to W, the distance between F and Q, and the state of the spindle obtained by operation or experiment, and analyzing the accumulated data. In this embodiment, the diagnosis unit 903 specifies the ratio of W to G (W / G) as the comparison result between G and W, but may specify the ratio of G to W (G / W). In this case, if the value of the comparison result between the specified G and W is less than a set threshold (e.g., 0.5, 0.33, etc.) and the value of the comparison result between the specified F and Q is equal to or greater than the set threshold, the diagnosis unit 903 diagnoses that an abnormality has occurred in the spindle connected to the roll supported by the measurement target chock.

[0130] In S1116, the output unit 904 outputs information indicating the result of the diagnosis of the spindle 202 in S1115. In this embodiment, the output unit 904 outputs the information indicating the result of the diagnosis of the spindle 202 by displaying it on the display device. As another example, the output unit 904 may output the information indicating the result of the diagnosis of the spindle 202 by storing it in the auxiliary storage device 803. The output unit 904 may output the information indicating the result of the diagnosis of the spindle 202 by transmitting it to a set destination such as an external server device.

[0131] (effect) As described above, in this embodiment, the information processing device 800 performed the diagnosis of the spindle using the rolling direction force, which is less likely to generate noise compared to sound and vibration. In addition, the information processing device 800 determines the coefficient α of the modified autoregressive model that approximates the measurement data by using some of the eigenvalues ​​of the autocorrelation matrix R so that more components useful for spindle diagnosis remain and less unuseful components remain. The information processing device 800 performed the diagnosis of the spindle using such a coefficient α. This allows the information processing device 800 to diagnose the spindle with greater accuracy than when diagnosis is performed using an acoustic or vibration signal that includes signal components in various frequency ranges.

[0132] (Variation 1) In this embodiment, the information processing device 800 diagnoses an abnormality in a spindle connected to a work roll of a rolling mill. However, as another example, the information processing device 800 may diagnose an abnormality in a spindle connected to a backup roll of a rolling mill. A backup roll is a roll for preventing the deflection of a work roll in a rolling mill. In that case, the information processing device 800 may diagnose an abnormality in a spindle connected to a backup roll of a rolling mill by replacing the chock supporting the work roll with a chock supporting the backup roll and performing a process similar to the process described in this embodiment. The work roll and the backup roll are each an example of a roll used in rolling a metal sheet.

[0133] (Variation 2) In this embodiment, the information processing device 800 performed diagnosis of a spindle to be diagnosed, by measuring the rolling direction force on a chock supporting the work side of a roll connected to the spindle to be diagnosed. However, depending on the abnormality of the spindle, a symptom of an abnormality may appear in the rolling direction force acting on the chock supporting the drive side of the roll connected to the spindle. Therefore, the information processing device 800 may diagnose the spindle by setting the chock supporting the drive side of the roll connected to the spindle to be diagnosed as the measurement target of the rolling direction force. In that case, the information processing device 800 performs the same processing as in Figs. 10 and 11, for example, by setting the measurement target chock as the chock (such as chock 101D) supporting the roll to which the spindle to be diagnosed is connected on the drive side.

[0134] (Variation 3) In this embodiment, m is a preset number of 100. However, the number of past data that can appropriately approximate the measurement data may be specified by performing an experiment or the like according to the diagnosis target, and the specified number may be used as the value of m. For example, the information processing device 800 may use, as m, the number of past measurement data used in approximation when the difference between the measurement data at a certain time and the measurement data at that time, which is approximated using a plurality of measurement data from the diagnosis target prior to that time and an autoregressive model or the like, is less than a set threshold value.

[0135] (Variation 4) In this embodiment, the information processing device 800 uses 1 as the number s of eigenvalues ​​to be used. However, as another example, the information processing device 800 may use the number s of eigenvalues ​​to be used determined as follows. That is, the information processing device 800 may use the smallest eigenvalue among a eigenvalues ​​of the autocorrelation matrix R whose sum of the largest a eigenvalues ​​is equal to or greater than a set percentage (e.g., 90%) of the sum of all the eigenvalues ​​of the autocorrelation matrix R as the number s of eigenvalues ​​to be used.

[0136] (Variation 5) In this embodiment, the information processing device 800 determines the coefficient α in the modified autoregressive model by using the eigenvalues, which are the number of eigenvalues ​​used, starting from the maximum, among the eigenvalues ​​of the autocorrelation matrix R. However, the information processing device 800 may determine the coefficient α in the modified autoregressive model by using any s eigenvalues ​​among the eigenvalues ​​of the autocorrelation matrix R. For example, the information processing device 800 may determine the coefficient α in the modified autoregressive model by using the maximum and the third largest eigenvalues ​​among the eigenvalues ​​of the autocorrelation matrix R.

[0137] (Variation 6) In this embodiment, the information processing device 800 d The spindle is diagnosed based on the comparison result between G and W and the comparison result between F and Q obtained by the decomposition of G and W, respectively. However, the information processing device 800 may diagnose whether the spindle is in a normal state by using another method. The inventors noticed the following by comparing the graphs in Fig. 4 with the graphs in Fig. 5. That is, the inventors noticed that the pattern of the coefficients of the modified autoregressive model corresponding to the spindle in which an abnormality occurs shows a waveform in which high frequency components stand out compared to the coefficients of the modified autoregressive model corresponding to the spindle in which no abnormality occurs. Therefore, the information processing device 800 may perform the following diagnostic process instead of that shown in FIG. 11. The information processing device 800 executes the same process as S1101 to S1105. Then, the diagnosis unit 903 interprets the coefficient α determined in S1104 and the teacher basis acquired in S1105 as time-series data including m (100) elements, and performs a Fourier transform on the coefficient α and the teacher basis. Then, the diagnosis unit 903 identifies a peak (a maximum value that is equal to or greater than a set threshold value) from the result of the Fourier transform of the teacher basis. The diagnosis unit 903 also identifies a peak (a maximum value that is equal to or greater than a set threshold value) from the result of the Fourier transform of the coefficient α. Then, when a peak with a lower frequency than the lowest frequency peak among the peaks identified from the result of the Fourier transform of the teacher basis exists among the peaks identified from the result of the Fourier transform of the coefficient α, the diagnosis unit 903 may diagnose that there is an abnormality in the spindle connected to the roll supported by the chock to be measured.

[0138] (Variation 7) In this embodiment, the information processing device 800 stores non-negative data indicating the pattern of the coefficient α in each column of the matrix Y d However, as another example, the information processing device 800 may generate a matrix Y such that non-negative data indicating the pattern of the coefficient α is stored in each row, not in each column. d In this case, the information processing device 800 may generate a matrix Y d , Y d =G T F T +W T Q T In this case, the information processing device 800 decomposes the cost function J d As a result, "FG+QW-Y" in Eq. d " to "G T F T +W T Q T -Y d " can be used as a function.

[0139] (Variation 8) In this embodiment, the information processing device 800 diagnoses whether the spindle to be diagnosed is in a normal state or not. However, the information processing device 800 may diagnose whether the spindle to be diagnosed is in another state (such as a scratched state, a cracked state, a broken state, a deformed state, a worn state, or a combination of these states). In that case, the information processing device 800 may, for example, in FIG. 10 , find a teacher basis for a target rolling mill whose spindles in the relevant state are spindle 202 and spindle 204, set a threshold value for the ratio of G to W and a threshold value for the distance between F and Q, and diagnose whether or not the relevant state is being reached. Also, for a plurality of states, a teacher basis may be obtained, the ratio of the weight of each teacher basis vector (each component of G) to W and the distance between each teacher basis vector (each column vector component of F) and Q may be derived, and a judgment criterion for the combination of these may be set to diagnose which of the plurality of states it is or is not. In this way, it is possible to suppress missed diagnosis of abnormalities similar to normal states in the teacher basis.

[0140] (Variation 9) In this embodiment, the information processing device 800 calculates a function J represented by Equation 16. d As a cost function, the information processing device 800 may use another function as a cost function as long as the function is an index for updating G, Q, and W. For example, the information processing device 800 may use a function J expressed by Equation 16 as a cost function. d A function expressed as the reciprocal of Y may be used as the cost function. In that case, the information processing device 800 updates the values ​​of G, Q, and W so that the value of the cost function increases in order to optimize (maximize) the value of the cost function. Then, when the cost function converges, the information processing device 800 determines that the value of the cost function has been optimized (maximized), and updates G, Q, and W at that time to Y d Alternatively, the decomposition result may be obtained as:

[0141] (Variation 10) In this embodiment, the information processing device 800 performs the diagnosis process of FIG. 11 by calculating the cost function J d The cost function J is calculated by repeating the update of G, Q, and W until the fluctuation of the value of is below a predetermined threshold a predetermined number of times. d The values ​​of G, Q, and W when the value of converges are obtained. However, as another example, the information processing device 800 may perform the following. That is, the information processing device 800 repeatedly updates G using formula 23, Q using formula 29, and W using formula 35, and calculates the Frobenius norms of matrices ΔG, ΔQ, and ΔW, which are the differences obtained by subtracting G, Q, and W before the updates from G, Q, and W after the updates, respectively, at each update stage. The information processing device 800 calculates the Frobenius norms of the cost function J at an update stage at which the ratios of the Frobenius norms of ΔG, ΔQ, and ΔW at each update stage to the Frobenius norms of ΔG, ΔQ, and ΔW at the first update stage are equal to or smaller than a predetermined threshold value. d It may be assumed that the value of J has converged. d When G, Q, and W converge, they are called the cost function J d Alternatively, the matrix that minimizes

[0142] (Other variations) Also, for example, some or all of the functions of the information processing device 800 described above may be implemented in the information processing device 800 as hardware. Furthermore, the above-described embodiments of the present invention are merely examples of the implementation of the present invention, and the technical scope of the present invention should not be interpreted as being limited by these. In other words, the present invention can be implemented in various forms without departing from its technical concept or main characteristics. [Explanation of symbols]

[0143] 800 Information Processing Equipment 801 CPU 901 Acquisition Department 902 Decision Section 903 Diagnostics Department 904 Output section

Claims

1. A rolling mill for rolling a metal plate, the rolling mill including a roll used for rolling the metal plate and a chock supporting the roll, and an acquisition means for acquiring measurement data indicating a force in a rolling direction applied to the chock, the measurement data being periodically measured during rolling of the metal plate using the rolling mill; A determination means for determining a correction coefficient, which is a coefficient in a corrected autoregressive model, based on the measurement data acquired by the acquisition means; a diagnostic means for diagnosing an abnormality in a spindle connected to the roll and used for rotating the roll, based on the correction coefficient determined by the determination means; having the corrected autoregressive model is an equation expressing a predicted value of the measurement data by using an actual value of the measurement data and the correction coefficient for the actual value, the determination means determines the correction coefficient using an equation in which a coefficient matrix is ​​a first matrix derived from a diagonal matrix having eigenvalues ​​of the autocorrelation matrix derived by performing singular value decomposition on the autocorrelation matrix derived from the measurement data as diagonal components, and an orthogonal matrix having eigenvectors of the autocorrelation matrix as column components, and the autocorrelation vector derived from the measurement data is a constant vector; the autocorrelation vector is a vector whose components are the autocorrelation of the measurement data from 1 to m, the number of the actual values ​​used in the corrected autoregressive model, The autocorrelation matrix is ​​a matrix whose components are the autocorrelation of the measurement data from time differences 0 to m−1, The first matrix is ​​a second matrix Σ derived from s eigenvalues ​​of the autocorrelation matrix and the diagonal matrix, where s is a set number equal to or greater than 1 and less than m. s and a third matrix U derived from the s eigenvalues ​​and the orthogonal matrix. s and the matrix U derived from s Σ s U s T and the second matrix is ​​a submatrix of the diagonal matrix and has the s eigenvalues ​​as diagonal elements; The device for diagnosing an abnormality in a spindle of a rolling mill, wherein the third matrix is ​​a submatrix of the orthogonal matrix and is a matrix having eigenvectors corresponding to the s eigenvalues ​​as column component vectors.

2. 2. The abnormality diagnosis device for a rolling mill spindle according to claim 1, wherein the diagnosis means decomposes a data matrix in which non-negative data indicating the correction coefficient determined by the determination means is stored, into a teacher basis matrix which is a non-negative matrix storing data indicating the correction coefficient corresponding to a predetermined state, a teacher weight matrix which is a non-negative matrix indicating weights of the teacher basis in the data matrix, an extraction basis matrix which is a non-negative matrix storing extraction bases extracted from the data matrix, and an extraction weight matrix which is a non-negative matrix indicating weights of the extraction bases in the data matrix, and diagnoses an abnormality in the spindle based on a comparison result between the teacher weight matrix and the extraction weight matrix and a comparison result between the teacher basis matrix and the extraction basis matrix.

3. 3. The abnormality diagnosis device for a rolling mill spindle according to claim 2, wherein the diagnosis means diagnoses that there is an abnormality in the spindle based on a ratio between the teacher weight matrix and the extraction weight matrix and a distance between the teacher basis matrix and the extraction basis matrix.

4. 4. The abnormality diagnosis device for a spindle of a rolling mill according to claim 1, wherein the s eigenvalues ​​include a maximum eigenvalue among the eigenvalues ​​of the autocorrelation matrix.

5. 5. The abnormality diagnosis device for a spindle of a rolling mill according to claim 4, wherein the s eigenvalues ​​are eigenvalues ​​selected in descending order from the eigenvalues ​​of the autocorrelation matrix.

6. 6. The abnormality diagnosis device for a rolling mill spindle according to claim 1, wherein the autocorrelation matrix is ​​a matrix included in a conditional equation that indicates a condition for minimizing a squared error between a predicted value of the measurement data and an actual value of the measurement data at a time corresponding to the predicted value of the measurement data.

7. 7. The abnormality diagnostic device for a spindle of a rolling mill according to claim 1, further comprising output means for outputting information relating to a result of the diagnosis by said diagnosing means.

8. 8. The abnormality diagnosis device for a spindle of a rolling mill according to claim 1, wherein the roll is a work roll that directly rolls the metal plate in the rolling mill.

9. A method for diagnosing an abnormality in a spindle of a rolling mill executed by an information processing device, comprising: An acquisition step of acquiring measurement data indicating a force in a rolling direction applied to the chock, the measurement data being periodically measured during rolling of the metal plate using a rolling mill including a roll used for rolling the metal plate and a chock supporting the roll; a determination step of determining correction coefficients, which are coefficients in a corrected autoregressive model, based on the measurement data acquired in the acquisition step; a diagnosis step of diagnosing an abnormality in a spindle connected to the roll and used to rotate the roll, based on the correction coefficient determined in the determination step; Including, the corrected autoregressive model is an equation expressing a predicted value of the measurement data by using an actual value of the measurement data and the correction coefficient for the actual value, In the determining step, a first matrix derived from a diagonal matrix having eigenvalues ​​of the autocorrelation matrix derived from the measurement data as diagonal components and an orthogonal matrix having eigenvectors of the autocorrelation matrix as column components is used as a coefficient matrix, and the correction coefficient is determined using an equation in which the autocorrelation vector derived from the measurement data is used as a constant vector; the autocorrelation vector is a vector whose components are the autocorrelation of the measurement data from 1 to m, the number of the actual values ​​used in the corrected autoregressive model, The autocorrelation matrix is ​​a matrix whose components are the autocorrelation of the measurement data from time differences 0 to m−1, The first matrix is ​​a second matrix Σ derived from s eigenvalues ​​of the autocorrelation matrix and the diagonal matrix, where s is a set number equal to or greater than 1 and less than m. s and a third matrix U derived from the s eigenvalues ​​and the orthogonal matrix. s and the matrix U derived from s Σ s U s T and the second matrix is ​​a submatrix of the diagonal matrix and has the s eigenvalues ​​as diagonal elements; The method for diagnosing an abnormality in a spindle of a rolling mill, wherein the third matrix is ​​a submatrix of the orthogonal matrix and has eigenvectors corresponding to the s eigenvalues ​​as column component vectors.

10. A program for causing a computer to function as each of the means of the abnormality diagnosis device for a spindle of a rolling mill according to any one of claims 1 to 8.

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