JP7610112B2 - Rolling mill spindle abnormality diagnosis device, method and program - Google Patents

Description

The present invention relates to an abnormality diagnosis device, method, and program for a spindle of a rolling mill .

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 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 an abnormality 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.

Japanese Patent Application Publication No. 7-265920 JP 2003-106946 A JP 2012-47639 A JP 2018-163135 A

There is a demand for a more accurate diagnosis of abnormalities in the spindles of rolls included in a rolling mill. However, the technology disclosed in Patent Document 1 diagnoses a load detection device, and is unable to diagnose abnormalities in the spindles that are connected to the rolls included in the rolling mill and used to rotate the rolls. Furthermore, the technology disclosed in Patent Documents 2 and 3 has 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.

The abnormality diagnosis device for a rolling mill spindle of the present invention includes: an acquisition means for acquiring measurement data indicating a force in a rolling direction applied to a chock used for rolling a metal plate using the rolling mill, the rolling mill including a roll used for rolling the metal plate and a chock supporting the roll; a determination 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 connected to the roll and used for rotating the roll, based on the correction coefficient determined by the determination means, wherein 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, The determination means determines the correction coefficients using an equation in which a first matrix derived from a diagonal matrix having eigenvalues of the autocorrelation matrix derived by singular value decomposition 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 a coefficient matrix and an autocorrelation vector derived from the measurement data is a constant vector, the autocorrelation vector being 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 being a matrix having autocorrelation of the measurement data from a time difference of 0 to m-1 as components, and the first matrix being 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. a matrix _{U s} Σ _s U _s ^T derived from the _s eigenvalues and the orthogonal matrix, the second matrix being a submatrix of the diagonal matrix and having the s eigenvalues as diagonal components, and the third matrix being a submatrix of the orthogonal matrix _and having eigenvectors corresponding to the s eigenvalues as column component vectors.

The present invention makes it possible to more accurately diagnose abnormalities in spindles that are connected to rolls included in a rolling mill and used to rotate the rolls.

FIG. 1 is a diagram illustrating an example of a rolling mill. FIG. 2 is a diagram illustrating an example of a rolling mill. FIG. 3 is a diagram illustrating an example of a distribution of eigenvalues. FIG. 4 shows the experimental results. FIG. 5 shows the experimental results. FIG. 6 shows the experimental results. FIG. 7 shows the experimental results. FIG. 8 is a diagram illustrating an example of a hardware configuration of an information processing device. FIG. 9 is a diagram illustrating an example of a functional configuration of an information processing device. FIG. 10 is a flowchart illustrating an example of processing by the information processing device. FIG. 11 is a flowchart illustrating an example of processing by the information processing device.

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

(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. The work roll is a roll that directly rolls a metal plate in a rolling mill. Abnormalities in the spindle include a state in which there is a flaw, a state in which there is a crack, a state in which there is a break, a state in which there is a deformation, a state in which there is a wear, a state in which there is a combination of these, and the like.

(Modified autoregressive model)
Here, the modified autoregressive model disclosed in Patent Document 4 will be described.
A value corresponding to a certain time k (1≦k≦M) in the time series data y is denoted as _yk . M is a number indicating up to what time the time series data y includes data. An autoregressive model approximating _yk is, for example, as shown in the following formula 1. As shown in formula 1, the autoregressive model is a formula that expresses a predicted value y^ _k (in the formula, ^ is written above y) of data at a certain time k (m+1≦k≦M) in the time series data, using an actual value _ykl of data at a time k-l (1≦l≦m) prior to that time in the time series data.

In Equation 1, α is a coefficient of the autoregressive model, and m is an integer less than M that indicates how many pieces of data prior to a certain time k are used to approximate y _k , which is the value of time-series data y at that time k in the autoregressive model.
Next, a conditional equation for approximating the predicted value y^ _k by the autoregressive model to the measured value _yk is obtained using the least squares method. As a condition for approximating the predicted value y^ _k by the autoregressive model to the measured value _yk , minimizing the squared error between y^ _k and _yk given by Equation 1 is considered. That is, in this experiment, the least squares method is used to approximate the predicted value y^ _k by the autoregressive model to _yk . The following Equation 2 is a conditional equation for minimizing the squared error between the time series data and the predicted value by the autoregressive model.

From equation 2, the relationship in equation 3 below is satisfied.

Furthermore, by transforming equation 3 (in matrix notation), we obtain the following equation 4.

R _jl in Equation 4 is called the autocorrelation of the time series data y, and is a value defined by the following Equation 5. In this case, |j-l| is called the time difference.

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 that predicted value, and is called the Yule-Walker equation. Equation 6 is also a linear equation whose variable vector is a vector made up 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.

Moreover, the autocorrelation matrix on the right side of Equation 6 (an m×m matrix composed of R _jl ) is expressed as an autocorrelation matrix R as shown in Equation 7 below.

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 components are emphasized (the signal-to-noise 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 Equation 8.

The matrix Σ in Equation 8 is a diagonal matrix whose diagonal components are eigenvalues of the autocorrelation matrix R, as shown in Equation 9. The diagonal components of the diagonal matrix Σ are σ ₁₁ , σ ₂₂ , ..., σ _mm . The matrix U is an orthogonal matrix whose column component vectors are eigenvectors of the autocorrelation matrix R. The column component vectors of the orthogonal matrix U are u ₁ , u ₂ , ..., u _m . There is a correspondence between the eigenvalue of the eigenvector u _j of the autocorrelation matrix R and σ _jj . The eigenvalue of the autocorrelation matrix R is a variable that reflects the sum of the intensities of the components of each frequency included in the time waveform of the predicted value of the time series data by the autoregressive model.

The values of σ ₁₁ , σ ₂₂ , ..., σ _mm, which are the diagonal components of the diagonal matrix Σ obtained as a result of singular value decomposition of the autocorrelation matrix R, are arranged in descending order to simplify the notation of the formula. Matrix R' is defined as shown in the following formula 10 using s eigenvalues, which is a set number that is equal to or greater than 1 and less than m, from the largest eigenvalue of these eigenvalues of the autocorrelation matrix R. Matrix R' is a matrix obtained by approximating the autocorrelation matrix R using s eigenvalues, which is the number of eigenvalues used, from the eigenvalues of the autocorrelation matrix R.

The matrix _Us in Equation 10 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 _Us is a submatrix composed of m×s elements from the left of the orthogonal matrix U. Also, _UsT is a transposed matrix of _Us , ^and is an s×m matrix composed of s row component vectors from the top of the matrix U ^T in Equation 8. The matrix _Σs in Equation 10 is an s×s matrix composed of s columns from the left and s rows from the top of the diagonal matrix Σ in Equation 8. That is, the matrix _Σs is a submatrix composed of s×s elements from the top left of the diagonal matrix Σ.
If the matrix Σ _s and the matrix U _s are expressed in terms of matrix elements, the following equation 11 is obtained.

By using matrix R' instead of autocorrelation matrix R, the relational equation in Equation 6 can be rewritten as Equation 12 below.

Equation 12 is transformed to obtain Equation 13 for calculating the coefficient α. A model for calculating the predicted value y^k using Equation 1 using the coefficient α calculated using Equation 13 is referred to as a "modified autoregressive model." In the modified autoregressive model, by using only some of the eigenvalues of the autocorrelation matrix R, the predicted value y _{^ k} can be calculated in a form in which the influence of noise is reduced.
Up to this point, the diagonal components σ ₁₁ , σ ₂₂ , ..., σ _mm of the diagonal matrix Σ have been described as being in descending order, but the diagonal components of the diagonal matrix Σ do not need to be in descending order in the process of calculating the coefficient α. In that case, the matrix U _s is a submatrix constructed by extracting the column component vectors (eigenvectors) corresponding to the eigenvalues to be used, rather than extracting the left m × s elements from the orthogonal matrix U, and the matrix Σ _s is a submatrix extracted so that the eigenvalues to be used are the diagonal components, rather than extracting the top left s × s elements from the diagonal matrix Σ.
Equation 13 is an equation used to determine the coefficients of the modified autoregressive model. The matrix _{Us in Equation 13 is a submatrix of an orthogonal matrix obtained by singular value decomposition of the autocorrelation matrix R, and is a third matrix that has eigenvectors corresponding to the eigenvalues to be used as column component vectors. The matrix Σs in} Equation 13 is a submatrix of a diagonal matrix obtained by singular value decomposition of the autocorrelation matrix R, and is a second matrix that has diagonal components that are _{eigenvalues to be used. The matrix UsΣsUsT} ⁱⁿ _Equation 13 is a first matrix that is derived from _{the matrix Σs and} the matrix _Us .

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 its coefficient is derived. In that case, the autocorrelation is expressed as the autocorrelation of a 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 to R _mm are autocorrelations with a time difference of 0, but these may be replaced with R ₁₁ .

(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 a 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.

First, the rolling mill used in this experiment (hereinafter, referred to as the "used rolling mill") will be described with reference to Figs.
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.

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 rolling the metal plate in cooperation. 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.

Load detection devices 102W and 103W are disposed 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 disposed at both ends of the chock 101D in the rolling direction. Load detection devices 107W and 108W are disposed 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 disposed at both ends of the chock 106D in the rolling direction.
Each of the load detection devices 102W, 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, 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, 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, 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.

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 viewed from the work side, the chock 101D, the load detection device 102D, the load detection device 103D, the measuring device 104D, the chock 106D, the load detection device 107D, the load detection device 108D, and the measuring device 109D are not shown.

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 any 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, when rolling 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.

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 performing singular value decomposition on 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, upon checking the graph in Fig. 3, noticed that there was one eigenvalue that was significantly higher than the other eigenvalues, and therefore set the number of eigenvalues (s) used in the modified autoregressive model to 1 in this experiment.

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 measurement data to fourth measurement data) as follows.
That is, the inventors defined the measurement data, which is time-series data, as y, and generated an autocorrelation matrix R using formulas 5 and 7. Then, the inventors subjected the generated R to singular value decomposition, and used s (1) eigenvalues among the obtained eigenvalues to obtain coefficients (α ₁ to α _m ) of the modified autoregressive model using formulas 5, 11, and 13. By substituting the coefficients obtained here into formula 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, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the first measurement data are referred to as the first coefficients. In the following, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the second measurement data are referred to as the second coefficients. In the following, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the third measurement data are referred to as the third coefficients. In the following, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the fourth measurement data are referred to as the fourth coefficients.
After the inventors determined the first to fourth coefficients, the rolling mill continued to operate. Then, the inventors confirmed that the spindle 204 had broken.

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, when rolling of a metal plate was being performed using a rolling mill in which the spindle 204 was 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.

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 formulas 5 and 7. Then, the inventors subjected the generated R to singular value decomposition, and used s (1) eigenvalues among the obtained eigenvalues to obtain coefficients (α ₁ to α _m ) of the modified autoregressive model using formulas 5, 11, and 13. By substituting the coefficients obtained here into formula 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, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the fifth measurement data are referred to as the fifth coefficients. In the following, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the sixth measurement data are referred to as the sixth coefficients. In the following, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the seventh measurement data are referred to as the seventh coefficients. In the following, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the eighth measurement data are referred to as the eighth coefficients.

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 coefficient to fourth coefficient) of a modified autoregressive model obtained from measurement data of rolling direction force for each chock of a rolling mill in which the spindle 204 is a deteriorated spindle. The pattern of the coefficients of the modified autoregressive model is information showing the shape when the components of the coefficients are arranged. Each graph in FIG. 5 is a graph showing a pattern of coefficients (fifth coefficient to eighth coefficient) of a modified autoregressive model obtained from measurement data of rolling direction force 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 coefficient. Moreover, the vertical axis of each graph in FIG. 4 and FIG. 5 indicates the value of the coefficient.

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, and the graph in Fig. 4(d) shows the pattern of the fourth coefficient.
The graph in Fig. 5(a) shows the pattern of the fifth coefficient, the graph in Fig. 5(b) shows the pattern of the sixth coefficient, the graph in Fig. 5(c) shows the pattern of the seventh coefficient, and the graph in Fig. 5(d) shows the pattern of the eighth coefficient.

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

The inventors compared the graphs of FIG. 4(b) and FIG. 5(b) and noticed that the graph of FIG. 4(b) shows a waveform that fluctuates significantly more than the graph of FIG. 5(b). The inventors also compared the graphs of FIG. 4(a) and FIG. 5(a) and noticed that the graph of FIG. 4(a) shows a waveform that fluctuates more than the graph of FIG. 5(a), although not as much as the difference between the graphs of FIG. 4(b) and FIG. 5(b). The inventors also compared the graphs of FIG. 4(c) and FIG. 5(c) and noticed that the graph of FIG. 4(c) shows a waveform that fluctuates more than the graph of FIG. 5(c), although not as much as the difference between the graphs of FIG. 4(b) and FIG. 5(b). The inventors compared the graphs in Figures 4(d) and 5(d) and noticed that the graph in Figure 4(d) exhibited a waveform that fluctuated more than the graph in Figure 5(d), although the difference was not as great as the difference between the graphs in Figures 4(b) and 5(b).

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 movement of the chock 106D in the rolling direction is restricted by the spindle 204.
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.

In this experiment, although not shown in FIG. 1, load detection devices are disposed 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) is connected to these load detection devices to measure the force in the gravity direction acting on the chock 106D from the load detected by these load detection devices (hereinafter referred to as the gravity direction force). Similarly, load detection devices are disposed 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) is connected to these load detection devices to measure the force in the gravity direction acting on the chock 106W from the load detected by these load detection devices.

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 cycle of 26 ms using the first gravity direction measurement device and the second gravity direction measurement device. In the following, the measurement data measured using the first gravity direction measurement device will be referred to as the ninth measurement data. Also, in the following, 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.

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, as follows.
That is, the inventors defined the measurement data, which is time-series data, as y, and generated an autocorrelation matrix R using equations 5 and 7. The inventors then subjected the generated R to singular value decomposition, and used s(1) eigenvalues among the obtained eigenvalues to find the coefficients (α ₁ to α _m ) of the corrected autoregressive model using equations 5, 11, and 13.
In the following, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the ninth measurement data are referred to as the ninth coefficients. Furthermore, in the following, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the tenth measurement data are referred to as the tenth coefficients. Furthermore, in the following, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the eleventh measurement data are referred to as the eleventh coefficients. Furthermore, in the following, the coefficients ( _α1 to _αm ) of the modified autoregressive model calculated from the twelfth measurement data are referred to as the twelfth coefficients.

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 shows the index of the coefficient. The vertical axis of each graph in Fig. 6 shows the value of the coefficient.
The graph in Fig. 6(a) shows the pattern of the 9th coefficient. The graph in Fig. 6(b) shows the pattern of the 10th coefficient. The graph in Fig. 6(c) shows the pattern of the 11th coefficient. The graph in Fig. 6(d) shows the pattern of the 12th coefficient.
The graphs in Figures 6(a) and 6(c) both show the coefficient patterns of the modified autoregressive model calculated from the measurement data of the gravity-direction force for the chock 106D. The graphs in Figures 6(b) and 6(d) both show the coefficient patterns of the modified autoregressive model calculated from the measurement data of the gravity-direction force for the chock 106W.

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.

The inventors, who confirmed that a pattern of coefficients of a modified autoregressive model obtained from measurement data of the rolling direction force on the chock indicates an abnormality in the spindle, came up with a method for diagnosing an abnormality in the spindle (hereinafter, referred to as an 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.

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).
The inventors used the non-negative matrix factorization described in WO 2019/026980 to determine an m (100) × 1 matrix that stores data indicating a pattern of coefficients corresponding to the chocks to be measured among the fifth to eighth coefficients. The matrix was determined as the teacher basis matrix F, which is a matrix indicating coefficients corresponding to a normal state.

In addition, the inventors performed q' times of measuring the rolling direction force of the measurement target chock periodically at least M times at a cycle of 26 [ms] while the rolling mill in use, 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.
The inventors then defined the measurement data as y for each of the acquired q' pieces of measurement data, and generated an autocorrelation matrix R using equations 5 and 7. The inventors then subjected the generated R to singular value decomposition, and used s(1) eigenvalues among the obtained eigenvalues to determine the coefficients (α ₁ to α _m ) of the corrected autoregressive model using equations 5, 11, and 13. The inventors then used the following equation 14 to determine a data matrix Y _d of m(100)×q'(1) that stores each element of the determined coefficients.

The data in each column of the matrix of Equation 14 indicates each of the coefficients α of the q' corrected autoregressive models obtained. That is, α _i , _j indicates the i-th element of the j-th coefficient α among the coefficients α of the q' corrected autoregressive models. In this experiment, since q' is 1, the coefficients (α ₁ to α _m ) of the corrected autoregressive model obtained are stored in Y _d as α _1,1 to α _m , _{1 ,} respectively.
In this experiment, the data matrix _Yd is decomposed into multiple matrices of non-negative values. In order to decompose the data matrix _Yd into multiple matrices of non-negative values, it is necessary to adjust each component of the matrix _Yd itself to a non-negative value without changing the pattern of the coefficient α of each column of the matrix _Yd . Therefore, the inventors ensured that each component of the data matrix _Yd is a non-negative value by subtracting the minimum value of the components of the matrix Yd from each component of _the data matrix _Yd . Each column of the adjusted data matrix _Yd stores non-negative data indicating the pattern of the coefficient α in the modified autoregressive model.
The inventors decomposed the adjusted data matrix _Yd into a plurality of non-negative matrices as shown in the following formula 15. More specifically, the inventors decomposed _Yd into a teacher basis matrix F, a teacher weight matrix G indicating weights for the teacher basis, an extraction basis matrix Q indicating an extraction basis that is a basis extracted from the data matrix _Yd, and an extraction weight matrix W indicating weights for the extraction basis, each of which is a non-negative matrix. The process of decomposing _Yd into F, G, Q, and W can be regarded as the following process. That is, the data of the coefficient α stored in each column of _Yd can be regarded as a process of decomposing the data into a weighted sum of a pattern indicated by the teacher basis 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 indicating the number of bases extracted from the data matrix (set to 1 in this experiment)). 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. In addition, 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 element in the j-th column in G indicates the weight of the component of the teacher basis included in the data indicating the pattern of the coefficient α stored in the j-th column of the adjusted data matrix Y _d. The value of the element in the i-th row and j-th column in _W indicates the weight of the component of the extraction basis stored in the i-th column of Q included in the data indicating the pattern of the coefficient α stored in the j-th column of the adjusted data matrix Y d.

A method for decomposing _Yd into F, G, Q, and W as shown in Equation 15 will be described.
The cost function J _d is defined as follows:

Fr in the first term on the right side of Equation 16 is a subscript indicating that it is a Frobenius norm. That is, the first term on the right side of Equation 16 is a Frobenius norm. The first term on the right side of Equation 16 indicates the magnitude of the difference between the sum of the product of F and G and the product of Q and W, and _Yd . The second term on the right side of Equation 16 is a term indicating a sparse constraint on the teacher weight matrix. δ ₁ in the second term on the right side of Equation 16 is a predetermined real number. k and t in the second term on the right side of Equation 16 are indexes indicating the rows and columns of the matrix, respectively.
The third term on the right side of Equation 16 is a term indicating a sparsity constraint on the extraction weight matrix. δ ₂ in the third term on the right side of Equation 16 is a predetermined real number. l and t in the third term on the right side of Equation 16 are indexes indicating the rows and columns of the matrix, respectively. The fourth term on the right side of Equation 16 is a term indicating an orthonormal constraint on the extraction basis (i.e., a constraint that all of the patterns stored in each column of the extraction basis matrix Q approximately form an orthonormal system). ε ₁ in the fourth term on the right side of Equation 16 is a predetermined real number. i and i′ in the fourth term on the right side of Equation 16 are indexes indicating the rows and columns 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 extraction basis (i.e., a constraint that the teacher basis matrix F and all of the patterns stored in each column of the extraction basis matrix Q are approximately orthogonal). ε ₂ in the fifth term on the right side of Equation 16 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 a matrix, respectively.
In this experiment, none of the following constraints are added: 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. That is, δ ₁ , δ ₂ , ε ₁ , and ε ₂ are each set to 0. Therefore, the cost function J _d is an equation consisting of only the first term on the right side of Equation 16.
By updating the values of G, Q, and W so as to optimize (minimize in this experiment) the value of _Jd , _Yd is decomposed into F, G, Q, and W. This involves solving the minimization problem of the cost function _Jd defined by the following equation 17.

In this experiment, the inventors performed the following operations to minimize the cost function _Jd . That is, the cost function _Jd is minimized by repeatedly updating G, Q, and W. In addition, in order to minimize the cost function _Jd , 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.
The update of G will now be described. In this experiment, G was updated as shown in the following formula 18.

In Equation 18, k and t are indices indicating the row and column of a matrix, respectively, and ^{η G} _kt is a non-negative value indicating the update step size for the k and t elements of G.
By partially differentiating the cost function J _d with respect to G, the following Equation 19 is obtained.

E ₃ in Equation 19 is a matrix of size 1×q′ in which all components are 1.
The inventors obtained the following Equation 20, which indicates G after the update, by substituting Equation 19 into Equation 18.

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 rightmost side of equation 20 excluding the last term 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 equation 21 below, so as to satisfy the condition that the rightmost side of equation 21 excluding the last term is 0.

From equation 21, η ^G _kt is given by equation 22 below.

By substituting equations 19 and 22 into equation 18, the inventors obtained the following equation 23, which shows the updated G.

That is, the inventors updated G using Equation 23 based on Y _d , F, G, Q, and W before the update at the time of processing, and a predetermined coefficient δ ₁ (0 in this experiment).
Next, a description will be given of updating Q. In this experiment, Q was updated as shown in the following formula 24.

In Equation 24, w and t are indices indicating the row and column of a matrix, respectively. ^{η Q} _wt is a non-negative value indicating the update step size for the w and t elements of Q.
By partially differentiating the cost function J _d with respect to Q, the following Equation 25 is obtained.

_E4 in Equation 25 is a matrix of size n×n where all components are 1. _E5 in Equation 25 is a matrix of size 1×1 where all components are 1.
By substituting Equation 25 into Equation 24, we obtain the following Equation 26, which indicates Q after the update.

Since 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 rightmost side of equation 26 excluding the last term is 0, then Q after the update will always be a non-negative value. For this reason, the inventors updated matrix Q as shown in equation 27 below, so as to satisfy the condition that the value of the rightmost side of equation 26 excluding the last term is 0.

From equation 27, η ^Q _wt is given by equation 28 below.

By substituting equations 25 and 28 into equation 24, the inventors obtained the following equation 29, which shows the updated G.

That is, Q was updated using Equation 29 based on _Yd , F, G, Q, and W before the update at the time of processing, and predetermined coefficients _ε1 and _ε2 (both 0 in this experiment).
Next, a description will be given of updating W. In this experiment, the inventors updated W as shown in the following formula 30.

In Equation 30, l and t are indices indicating the row and column of the matrix, respectively. ^{η W} _lt is a non-negative value indicating the update step size for the l and t elements of W.
The inventors obtained the following Equation 31 by partially differentiating the cost function J _d with respect to W.

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 indicates the updated W.

Since 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 rightmost side of equation 32 excluding the last term is 0, then W after the update will always be a non-negative value. For this reason, the inventors updated matrix W so as to satisfy the condition that the rightmost side of equation 32 excluding the last term is 0, as shown in equation 33 below.

From equation 33, η ^W _lt is expressed as equation 34 below.

By substituting equations 31 and 34 into equation 30, the inventors obtained the following equation 35, which shows the updated W.

That is, the inventors updated G using Equation 35 based on Y _d , F, G, Q, and W before the update at the time of processing, and a predetermined coefficient δ ₂ (0 in this experiment).
As described above, in this experiment, the inventors repeatedly updated G using Equation 23, updated Q using Equation 29, and updated W using Equation 58, and 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, at each update stage. The inventors determined that the value of the cost function Jd converged at an update stage at which 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 was equal to or less than a predetermined threshold. Then, G, Q, and W at _the time when _Jd converged were determined as matrices that minimize the cost function _Jd . As a result, the inventors decomposed _Yd into F, G, Q, and W, which are non-negative matrices, as shown in Equation 15.
In this experiment, G, Q, and W that minimize the cost function _Jd are obtained as described above. However, as another example, the update of G using formula 23, the update of Q using formula 29, and the update of W using formula 35 may be repeated, and the value of the cost function _Jd may be deemed to have converged if the fluctuation in the value of the cost function _Jd before and after the update of G, Q, and W is equal to or less than a predetermined threshold value for a predetermined number of consecutive times. Then, G, Q, and W when _Jd has converged may be matrices that minimize the cost function _Jd .

The following describes F, G, Q, and W obtained when the measurement target chock is the chock 106D (when F indicates the pattern of the fifth coefficient and _Yd indicates the pattern of the first coefficient). The teacher basis vector F and the 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 was 0.04×10 ⁻⁴ . W was 0.68×10 ⁻⁴ .
Since the weighting coefficient W of the extracted basis vector Q is 10 times or more larger than the weighting coefficient G of the teacher basis vector F, the inventors noticed that the first coefficient indicates a pattern closer to the extracted basis vector Q than to the teacher basis vector F. Furthermore, the inventors defined 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 the elements with the same index in F and Q, i.e., the ^L1 distance), which was found to be 0.770.

The following describes F, G, Q, and W obtained when the chock to be measured is the chock 106W (when F indicates the pattern of the sixth coefficient and _Yd indicates the pattern of the second coefficient). The teacher basis vector F and the 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 was 0.72×10 ⁻⁴ . W was 1.37×10 ⁻⁴ .
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 indicates a pattern closer to the extracted basis vector Q than to the teacher basis vector F. Furthermore, the inventors found that the distance between the teacher basis vector F and the extracted basis vector Q (Σ _(i=1) ^m |F(i)-Q(i)|) was 2.20.

The following describes F, G, Q, and W obtained when the measurement target chock is the chock 101D (when F indicates the pattern of the seventh coefficient and _Yd indicates the pattern of the third coefficient). The teacher basis vector F and the extracted basis vector Q are as shown in FIG. 7(c). The horizontal axis of the graph in FIG. 7(c) indicates the index of the basis vector (coefficient of the modified autoregressive model). The vertical axis of the graph in FIG. 7(c) indicates the value of the basis vector (coefficient of the modified autoregressive model). The solid line pattern in the graph in FIG. 7(c) indicates the pattern of the teacher basis vector F. The dashed line pattern in the graph in FIG. 7(c) indicates the pattern of the extracted basis vector Q. G was 1.21×10 ⁻⁴ . W was 0.42×10 ⁻⁴ .
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.

The following describes F, G, Q, and W obtained when the measurement target chock is the chock 101W (when F indicates the pattern of the eighth coefficient and _Yd indicates the pattern of the fourth coefficient). The teacher basis vector F and the extracted basis vector Q are as shown in FIG. 7(d). The horizontal axis of the graph in FIG. 7(d) indicates the index of the basis vector (coefficient of the modified autoregressive model). The vertical axis of the graph in FIG. 7(d) indicates the value of the basis vector (coefficient of the modified autoregressive model). The solid line pattern in the graph in FIG. 7(d) indicates the pattern of the teacher basis vector F. The dashed line pattern in the graph in FIG. 7(d) indicates the pattern of the extracted basis vector Q. G was 2.22×10 ⁻⁴ . W was 0.83×10 ⁻⁴ .
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.

As shown in Fig. 4B, 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 normal spindle of a work roll 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 in the rolling mill. Then, when a rolling mill with an unknown spindle state is rolling a metal plate, a data matrix _Yd is generated from the measurement data of the rolling direction force applied to the chock, and the generated data matrix _Yd 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, based on the comparison result between the teacher weighting coefficient and the extracted weighting coefficient obtained by the decomposition of the data matrix _Yd and the comparison result between the teacher basis vector and the extracted basis vector, it is diagnosed whether the state of the spindle connected to the work roll supported by the chock is normal or not.

(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 having 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 for pressing the chocks of the work rolls in the rolling direction, such as a mill stabilizer), 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 to each other via a system bus 807 so as to be able to communicate with each other.

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 as another example, it may be another storage device such as a ROM (Read Only Memory) or an SSD (Solid State Drive). 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, 109D) that measures the rolling direction force applied to the chock of the target rolling mill.

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, the output device 806 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.

(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 measurement data of the rolling direction forces from each of the measuring devices 104W, 104D, 109W, and 109D via the device I/F 804.

The determining unit 902 determines the coefficients of a modified autoregressive model that predicts a predicted value of the measurement data acquired by the acquiring unit 901. The modified autoregressive model is Equation 1 that expresses a predicted value y^k of y using actual values yk _-1 to _ykm of the measurement data y and coefficients α (= _α1 to _αm ) for these actual values. The 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) that extracts components useful for diagnosing an abnormality 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 of 0 to m-1, is used as a coefficient matrix, and the autocorrelation vector, whose components are the autocorrelation of y with time lags of 1 to m, is used as a constant vector.

Equation 6 can be derived as a conditional equation indicating a condition for minimizing the square error between the predicted value y^ _k of y calculated by Equation 1 and the actual measured value yk of y at time _k corresponding to the predicted value y^ _k of y. The first matrix R' is derived from a diagonal matrix Σ having eigenvalues of the autocorrelation matrix R derived by performing singular value decomposition (Equation 8) as diagonal components, and an orthogonal matrix U having eigenvectors of the autocorrelation matrix R as column components. The first matrix R' is a matrix U s Σ s U s T derived from a submatrix of the diagonal matrix Σ having eigenvalues of the number s of used eigenvalues as diagonal components, and a submatrix of the orthogonal matrix U having eigenvectors corresponding to the number _s of used eigenvalues as column component vectors, using eigenvalues of the number s of used eigenvalues set to be 1 _or more and less than _m , among the _eigenvalues of the autocorrelation _matrix ^R. The number s of eigenvalues to be used may be any number that includes the maximum eigenvalue of the autocorrelation matrix R, and it is preferable that the eigenvalues are selected in descending order of value.

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 .

(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, the information 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 of 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.

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 determining unit 902 performs singular value decomposition on the matrix R found in S1002 to obtain the orthogonal matrix U and diagonal matrix Σ of Equation 8, and obtains the eigenvalues σ ₁₁ to σ _mm of the autocorrelation matrix R from the diagonal matrix Σ.

In S1004, the determination unit 902 selects, from among the multiple eigenvalues σ ₁₁ to σ _mm of the matrix R determined in S1002, the largest eigenvalues σ ₁₁ to σ _ss , the number s of eigenvalues to be used, as eigenvalues of the autocorrelation matrix R to be used to determine the coefficient α of the modified autoregressive model. In this embodiment, the number s of eigenvalues to be used is 1, but may be 2 or more. Then, the determination unit 902 determines the coefficient α of the modified autoregressive model using Equation 13, based on the selected eigenvalues σ ₁₁ to σ _ss , the corresponding measurement data y, and the orthogonal matrix U obtained by singular value decomposition of the autocorrelation matrix R.
Then, the determination unit 902 determines an m×1 matrix storing the coefficient α calculated for the matrix R calculated in S<b>1002 as a teacher basis matrix, and stores information about the teacher basis matrix in the auxiliary storage device 803 .

(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.

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 with 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.

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 determining 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 obtains the eigenvalues σ ₁₁ to σ _mm of the autocorrelation matrix R from the diagonal matrix Σ.

In S1104, the determination unit 902 selects the largest eigenvalues σ ₁₁ to σ _ss , which are the number s (one) of eigenvalues used, from among the multiple eigenvalues σ ₁₁ to σ _mm of R acquired in S1103, as the eigenvalues of R to be used to determine the coefficient α of the modified autoregressive model. The determination unit 902 then determines the coefficient α of the modified autoregressive model using Equation 13 based on the measurement data y corresponding to this R, the eigenvalues σ ₁₁ to σ _ss , and the orthogonal matrix U obtained by singular value decomposition of this R. The coefficient α determined in S1104 is an example of a correction coefficient, which is a coefficient in the modified autoregressive model determined from the measurement data.

In S1105, the diagnosis unit 903 acquires the teacher basis matrix (the teacher basis matrix corresponding to the measurement target chock) stored in S1004 from the auxiliary storage device 803.
In S1106, the diagnosis unit 903 uses the coefficients determined in S1104 as α (α ₁ to α _m ) to generate a data matrix Y _d of size m×q′ as shown in Equation 37 using α. In this embodiment, q′ is 1. More specifically, the diagnosis unit 903 generates Y _d by substituting α ₁ to α _m into α ₁ , ₁ to α _m , ₁ in Equation 37, respectively. That is, each column of the data matrix Y _d stores data of this coefficient. In addition, the diagnosis unit 903 converts each component of the generated data matrix Y _d into a non-negative value. In this embodiment, the diagnosis unit 903 performs a process of subtracting the minimum value of the components of the matrix Y _d from each component of the matrix Y _d .

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. 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 _d . The diagnosis unit 903 also generates a matrix Q (in this embodiment, a vector) of size m×(a predetermined number n) that stores the extraction basis matrix, which is a pattern extracted from the data matrix Y _d . In this embodiment, n is set to 1, and the extraction basis matrix is extracted from the data matrix Y _d . The diagnosis unit 903 also generates an extraction weight matrix W (in this embodiment, a scalar value) of size n(1)×q′(1) that stores the weights of the components of the extraction basis included in the data matrix Y _d .
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.

In S1108, the diagnosis unit 903 obtains the value of the cost function Jd as the cost using Equation 39 based on _Yd , F, G, Q, _W , and predetermined coefficients _δ1 , _δ2 , _ε1 , and _{ε2. In this embodiment, the values of δ1, δ2, ε1 , and ε2 are} each set to 0. The diagnosis unit 903 stores the obtained cost in the main storage device 802 as the pre-update cost.
In S1109, the diagnosis unit 903 updates each of G, Q, and W. More specifically, the diagnosis unit 903 updates G using Equation 46 based on _Yd , F, G, Q, and W before the update, a predetermined coefficient δ ₁ (0 in this embodiment), and E ₃ which is a matrix of size 1×q′ with all components being 1. However, since δ ₁ is 0 in this embodiment, the diagnosis unit 903 may update G without using E ₃ .

Furthermore, the diagnosis unit 903 updates Q using Equation 52 based on _Yd , F, G, Q, and W before the update, predetermined coefficients _ε1 and _ε2 (both 0 in this embodiment), _E4 which is a matrix of size n×n with all components being 1, and E5 which is a matrix of size 1×1 with all components being 1. However, since _ε1 and _ε2 are both 0 in this embodiment, the diagnosis unit ₉₀₃ may update Q without using _E4 and _E5 .
Furthermore, the diagnosis unit 903 updates W using Equation 58 based on _Yd , F, G, Q, and W before the update, a predetermined coefficient δ ₂ (0 in this embodiment), and E6 which is a matrix of size 1×q′ with all components being 1. However, since δ ₂ is 0 in this embodiment, the diagnosis unit 903 may update Q without using E6.

In S1110, the diagnosis unit 903 obtains the value of the cost function Jd as a cost based on _Yd , F, G, Q, and W updated in S1109, and the coefficients _δ1 , _δ2 , _ε1 , and _ε2 using Equation 39. The diagnosis unit 903 stores the obtained cost in the main memory device ₈₀₂ as the 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.

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 starting the process of 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 determines whether the counter value stored in the main memory device 802 is equal to or greater than a predetermined threshold. If the diagnosis unit 903 determines that the counter value stored in the main memory device 802 is equal to or greater than the predetermined threshold, it determines that the value of the cost function _Jd has converged to a minimum value, and proceeds to S1115. If the diagnosis unit 903 determines that the counter value is less than the predetermined threshold, it proceeds to S1109.

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)|) as a comparison result between F and Q, both of which are m×1 matrices ( _i.e. , vectors). If the identified value of the comparison result between G and W is equal to or greater than a set threshold value (e.g., 2.0, 3.0, etc.) and the identified value of the comparison result between F and Q is equal to or greater than a set threshold value (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. Furthermore, when the value of the comparison result between the identified G and W is less than a set threshold value, or the value of the comparison result between the identified F and Q is less than a set threshold value (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 threshold values may be set according to the management criteria by accumulating data on the ratio between G and W, the distance between F and Q, and the state of the spindle obtained through operations or experiments, 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, when the value of the comparison result between the specified G and W is less than a set threshold value (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 value, the diagnosis unit 903 diagnoses that an abnormality has occurred in the spindle connected to the roll supported by the measurement target chock.

In S1116, the output unit 904 outputs information indicating the results of the diagnosis of the spindle 202 in S1115. In this embodiment, the output unit 904 outputs the information indicating the results 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 results 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 results of the diagnosis of the spindle 202 by transmitting it to a set destination such as an external server device.

(effect)
As described above, in this embodiment, the information processing device 800 performed spindle diagnosis using the rolling direction force, which is less likely to generate noise than 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 fewer components that are not useful remain. The information processing device 800 performed spindle diagnosis using such 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.

(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.

(Variation 2)
In this embodiment, the information processing device 800 performed diagnosis of the spindle to be diagnosed, by measuring the rolling direction force on the chock supporting the work side of the 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 (e.g., chock 101D) supporting the roll to which the diagnosis target spindle is connected on the drive side.

(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, which is approximated using a plurality of measurement data from the past before that time and the measurement data at that time, is less than a set threshold value.

(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 total of the largest a eigenvalues is equal to or greater than a set percentage (e.g., 90%) of the total value of all eigenvalues of the autocorrelation matrix R as the number s of eigenvalues to be used.

(Variation 5)
In this embodiment, the information processing device 800 determines the coefficient α in the modified autoregressive model by using the eigenvalues of the autocorrelation matrix R, starting from the largest eigenvalue. However, the information processing device 800 may determine the coefficient α in the modified autoregressive model by using any s 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 largest and the third largest eigenvalues of the autocorrelation matrix R.

(Variation 6)
In this embodiment, the information processing device 800 diagnoses the spindle based on the comparison result between G and W obtained by decomposing _Yd and the comparison result between F and Q. However, the information processing device 800 may diagnose whether the spindle is in a normal state by using another method.
The inventors have noticed the following by comparing the graphs in Fig. 4 with the graphs in Fig. 5. That is, the inventors have 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. Also, 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 coefficient α. Then, 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 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 is present among the peaks identified from the result of the Fourier transform of the coefficient α.

(Variation 7)
In this embodiment, the information processing device 800 generates the matrix _Yd so that non-negative data indicating the pattern of the coefficient α is stored in each column. However, as another example, the information processing device 800 may generate the matrix _Yd so that non-negative data indicating the pattern of the coefficient α is stored in each row instead of each column. In that case, the information processing device 800 may decompose the matrix _Yd as _Yd = G ^T F ^T + W ^T Q ^T. In that case, the information processing device 800 may use a function in which the part of "FG + QW - _Yd " in Equation 39 is replaced with "G ^T F ^T + W ^T Q ^T - _Yd " as the cost function _Jd .

(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, a teacher basis may be obtained for a plurality of states, 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 the state is in or which is not in. In this way, it is possible to suppress missed diagnosis of abnormalities similar to normal states in the teacher basis.

(Variation 9)
In this embodiment, the information processing device 800 uses the function _Jd expressed by Equation 16 as the cost function. However, the information processing device 800 may use other functions as the cost function as long as the functions are indices for updating G, Q, and W. For example, the information processing device 800 may use a function expressed by the inverse of the function _Jd expressed by Equation 16 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 may acquire G, Q, and W at that time as the decomposition result of _Yd , assuming that the value of the cost function has been optimized (maximized).

(Variation 10)
In this embodiment, the information processing device 800 repeats updating G, Q, and W until the fluctuation in the value of the cost function _Jd before and after the update of G, Q, and W becomes equal to or smaller than a predetermined threshold value a predetermined number of times in succession in the diagnosis process of Fig. 11, thereby obtaining G, Q, and W when the value of the cost function _Jd has converged. However, as another example, the information processing device 800 may be as follows.
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 these matrices for 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, respectively, at each update stage. The information processing device 800 may determine that the value of the cost function _Jd has converged at an update stage at which 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 less than a predetermined threshold. Then, the information processing device 800 may obtain G, Q, and W when _Jd has converged as matrices that minimize the cost function _Jd .

(Other Modifications)
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 features.

800 Information processing device 801 CPU
901 Acquisition unit 902 Decision unit 903 Diagnosis unit 904 Output unit

Claims (10)

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 matrix UsΣsUsT derived from: a second matrix _Σs derived from s eigenvalues of the autocorrelation matrix and the diagonal matrix, and a third matrix Us derived from the s eigenvalues and the orthogonal matrix, where _s is a set number equal to or _{greater than} 1 ^and less than _m ;
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. 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. 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. 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. 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. 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. 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. 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. 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 matrix UsΣsUsT derived from: a second matrix _Σs derived from s eigenvalues of the autocorrelation matrix and the diagonal matrix, and a third matrix Us derived from the s eigenvalues and the orthogonal matrix, where _s is a set number equal to or _{greater than} 1 ^and less than _m ;
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. 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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