JP7014080B2 - Information processing equipment, information processing methods and programs - Google Patents

Description

The present invention relates to an information processing apparatus, an information processing method and a program.

As a technique for diagnosing anomalies in a moving object, the signal obtained from the moving object is measured, and the object is normal or abnormal based on the temporal transition of the amplitude in the signal. There is a method of determining whether or not it is.
In Patent Document 1, a signal in the frequency band required for diagnosis is extracted from the detected signal, an envelope signal of the extracted signal is obtained, the frequency band of the obtained envelope signal is lowered, and the band is lowered. A system for thinning out an envelope signal, frequency-analyzing the thinned-out envelope signal, and diagnosing an abnormality based on the analysis result is disclosed.

Japanese Unexamined Patent Publication No. 2006-11003

In the method disclosed in Patent Document 1, diagnosis is performed by performing frequency analysis on an envelope signal whose band has been lowered by applying a low-pass filter. The cutoff frequency in the low-pass filter is qualitatively determined by the user. However, when a low-pass filter is used, an important signal may be attenuated depending on the cutoff frequency, and the signal may not be detected. Therefore, in Patent Document 1, there is a limit to the accuracy of diagnosis.
The present invention has been made in view of the above problems, and an object of the present invention is to enable more accurate diagnosis of an abnormality of an object that undergoes periodic motion.

The information processing apparatus of the present invention is an acquisition means for acquiring transition data showing the state of temporal transition of the amplitude of the measurement data based on the measurement data related to the periodic movement of the object performing the periodic movement. And, the determination means for determining the coefficient in the modified self-return model based on the transition data acquired by the acquisition means, and the abnormality of the object is diagnosed based on the coefficient determined by the determination means. The modified self-return model is an expression representing a predicted value of the transition data using the actual value of the transition data and the coefficient with respect to the actual value. The determination means is a column of a diagonal matrix having an eigenvalue of the autocorrelation matrix derived by singular value decomposition of the autocorrelation matrix derived from the transition data and an eigenvector of the autocorrelation matrix. The coefficient is determined using an equation in which the orthogonal matrix as a component and the first matrix derived from the coefficient matrix are used and the eigenvalue vector derived from the transition data is a constant vector, and the eigenvalue vector is determined. Is a vector whose component is the autocorrelation of the transition data from 1 to m, which is the number of the actual values used in the modified self-return model, and the autocorrelation matrix has a time difference of 0 to 0. It is a matrix whose component is the autocorrelation of the transition data up to m-1, and the first matrix is diagonal to the s eigenvalues determined as the dominant eigenvalues among the eigenvalues of the autocorrelation matrix. The second matrix Σ _s derived from the matrix, the third matrix Us derived from the _s eigenvalues and the orthogonal matrix, and the matrix _Us Σ _{s Us} ^T derived from the matrix. The second matrix is a submatrix of the diagonal matrix and has s eigenvalues as diagonal components, and the third matrix is a submatrix of the orthogonal matrix. , The eigenvector corresponding to the s eigenvalues is a matrix whose column component vector is used.

INDUSTRIAL APPLICABILITY According to the present invention, it is possible to provide a technique capable of more accurately diagnosing an abnormality of an object that performs periodic motion.

FIG. 1 is a diagram showing the situation of the experiment. FIG. 2 is a diagram illustrating a detailed example of the bearing. FIG. 3 is a diagram showing an example of the distribution of eigenvalues. FIG. 4 is a diagram showing an example of a waveform of measurement data. FIG. 5 is a diagram showing an example of the power spectrum of the transition data. FIG. 6 is a diagram showing an example of a data power spectrum consisting of predicted values of transition data obtained by a modified autoregressive model. FIG. 7 is a diagram showing an example of the power spectrum of the transition data. FIG. 8 is a diagram showing an example of a data power spectrum consisting of predicted values of transition data obtained by a modified autoregressive model. FIG. 9 is a diagram showing an example of a power spectrum of transition data to which a low-pass filter is applied. FIG. 10 is a diagram showing an example of a system configuration of a diagnostic system. FIG. 11 is a diagram showing an example of the hardware configuration of the information processing apparatus. FIG. 12 is a flowchart showing an example of processing of the information processing apparatus.

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

(Outline of processing of this embodiment)
In this embodiment, a process of diagnosing an abnormality of a bearing based on a vibration signal measured from a bearing used in a railroad bogie by a diagnostic system will be described.
The diagnostic system measures the signal corresponding to the vibration of the bearing, acquires the transition data which is a signal showing the state of the temporal transition of the amplitude in the signal based on the measured signal, and acquires the acquired transition data. Expressed as a self-return model, the matrix in the conditional expression related to the coefficient of the self-return model is decomposed into singular values, the eigenvalues of the matrix are obtained, the dominant eigenvalue is determined from the obtained eigenvalues, and the determined dominant eigenvalues are used. To determine the coefficients of the self-return model. Then, the diagnostic system obtains the predicted value of the transition data by the modified autoregressive model specified by the determined coefficient, and diagnoses the abnormality of the bearing based on the power spectrum of the data consisting of the predicted value of the transition data. ..

(Diagnosis experiment of bearing abnormality)
An experiment conducted to evaluate the accuracy of abnormality diagnosis of bearings used in railway bogies will be described.
FIG. 1A is a diagram illustrating the situation of this experiment. The situation of FIG. 1A is a situation in which a wheel drive mechanism in a railroad bogie is installed in a laboratory. The drive motor 101 rotates the small gear 105 via the drive motor shaft 102, the gear joint 103, and the small gear shaft 100. The small gear 105 rotates to rotate the large gear 107. Axle 109 rotates accordingly, and the wheels connected to the axle 109 rotate. In this experiment, a dynamo 110 is connected to the axle 109 instead of a wheel. The dynamo 110 is a generator connected to give a pseudo running load. In this experiment, the load for rotating the dynamo 110 is assumed as the load during running.
The small gear shaft 100 to which the small gear 105 is fitted and the axle 109 to which the large gear 107 is fitted are fixed to the gear box 104. A bearing 106 is mounted between the gear box 104 and the small gear shaft, and a bearing 108 is mounted between the gear box 104 and the axle 109. FIG. 1B is a view showing a state of the bearing attached to the gear box 104 as viewed from the side surface.

The position 111 on the gear box 104 is the position where the vibration measuring device is installed. The vibration measuring device includes sensors such as an acceleration sensor and a laser displacement meter, detects the vibration of an object via the sensor, and outputs a signal corresponding to the detected vibration. The vibration measuring device installed at the position 111 measures the vibration transmitted to the position 111, and outputs a signal indicating the measured vibration to an external information processing device or the like via wired or wireless communication. In this experiment, the vibration measuring device is installed at the position 111, but it may be installed at any position as long as the vibration caused by the bearing 106 is transmitted.
Here, the bearing 106 will be described. FIG. 2 is a diagram illustrating a configuration of an example of the bearing 106. The bearing 106 is composed of four parts: an outer ring, an inner ring, a rolling element, and a cage. FIG. 2 shows an outline of the outer ring, the inner ring, the rolling element, and the cage of the bearing 106. The bearing 106 is configured such that a rolling element held by a cage is sandwiched between the outer ring and the inner ring.
In this experiment, as the bearing 106 mounted on the small gear 105, a normal bearing without flaws and a bearing with flaws on the outer ring were used. For bearings with flaws on the outer ring, it was also confirmed that there were no other types of flaws. The drive motor 101 was driven for each bearing 106, and the vibration measuring device installed at the position 111 measured the vibration, thereby acquiring the measurement data for diagnosing the abnormality of the bearing 106. In this experiment, the drive motor 101 was driven so that the rotation speed of the inner ring of the bearing 106 was 3000 rpm (round per minute). Further, the fundamental frequency corresponding to the rotation cycle of the flaw in the outer ring of the bearing 106 is about 260 Hz. Further, the signal related to the flaw attached to the outer ring of the bearing 106 is a signal obtained by superimposing a signal having this fundamental frequency and a signal (harmonic) that is an integral multiple of the signal having this fundamental frequency (for example, a square wave). Is known to be. Therefore, when a signal of about 260 Hz and a signal of an integral multiple of about 260 Hz are detected, it can be diagnosed that a flaw exists in the outer ring of the bearing 106.
As described above, the measurement data of the vibration at the position 111 was acquired when the bearing 106 was normal and when the outer ring of the bearing 106 had a defect.

Next, a method of diagnosing an abnormality of the bearing 106 using the measurement data measured by the vibration measuring device will be described. In the following, the measurement data measured by the vibration measuring device will be referred to as measurement data v. From this measurement data v, it was decided to obtain the transition data y indicating the temporal transition of the amplitude in the measurement data v. In this experiment, the envelope of the measurement data v was obtained as the transition data y.
Here, a method of obtaining the envelope of the measurement signal v based on the measurement signal v will be described.
The envelope is defined as the instantaneous amplitude of the analysis signal of the measurement signal, assuming that the measurement signal is a real signal (a real function of time t) whose amplitude and angular frequency change with time. The analysis signal v _a of the measurement signal v is a complex signal (complex function at time t) defined by the following equation 1.

Here, i is an imaginary unit, and v ^ (^ is expressed above v in the equation) is a real signal defined by the following equation 2, which is called the Hilbert transform of v. be.

Here, π is the pi. The envelope v _m of the measurement signal v is a real signal defined by the following equation 3.

The analytic signal v _a does not necessarily have to be calculated by Equation 2, and can be calculated relatively easily by the following procedure using the Fourier transform (FFT). First, the Fourier transform V of the measurement signal v is obtained. Next, the Fourier transform Va _a of the analysis signal v _a is obtained using the following equation 4. Finally, the inverse Fourier transform is applied to _{Va to obtain the analysis signal v a .}

The v _m (t) shown in the equation 3 is a signal called the envelope of v, and is an example of a signal showing the state of the temporal transition of the amplitude in the measurement signal v.
In this experiment, the analysis signal v _a was calculated from the measurement data v by the method using the above-mentioned Fourier transform, and the envelope (v _m (t)) of v was obtained as the transition data y using the equation 3. In addition to the envelope, the transition data includes the following signals.
The data obtained by multiplying the envelope (vm ( _t )) by a positive real number is an example of transition data. This is because the value itself at each time is not important because the transition data only needs to show the transition of the value over time. Further, the data obtained by adding a predetermined value to the value at each time of the envelope (vm ( _t )) is also an example of the transition data.
Further, for example, for the portion where the value in v (t) is negative, a function v'(t) = | v (t) | which is multiplied by -1 to obtain a positive value is assumed, and about this v'(t). A signal obtained by applying a low-pass filter that cuts a signal having a frequency equal to or higher than a predetermined threshold value is also an example of transition data showing the temporal transition of the amplitude of v. Further, by specifying the mountain part in the function v'(t) and interpolating the specified part (for example, polynomial interpolation), the signal indicated by the obtained function also shows the state of the temporal transition of the amplitude of v. This is an example of transition data.

The transition data y can be regarded as data in which the relatively high frequency component in the measurement data v is removed and the characteristics of the relatively low frequency component remain. Therefore, when an abnormality occurs in the bearing 106, in the transition data y, for example, a signal having a relatively low frequency in the measurement data v corresponding to the abnormality occurring in the bearing 106 (for example, a signal related to the rotation cycle of the flaw) is displayed. It will be emphasized. Therefore, for example, when the signal generated by the abnormality of the bearing 106 does not appear at a relatively high frequency and appears at a relatively low frequency as compared with the natural frequency of the flaw, it is generated at the bearing 106 by using the transition data y. It will be possible to diagnose abnormalities.
Subsequently, in this experiment, the predicted value of the transition data was obtained from the transition data y by the modified autoregressive model, and the feature amount was calculated from the data consisting of the predicted values of the transition data.
Let y _k be the value of the transition data y at a certain time k (1 ≦ k ≦ M). M is a number indicating to which time the transition data y includes the data, and is set in advance. An autoregressive model that approximates y _k is, for example, Equation 5 below. As shown in Equation 5, the autoregressive model is a predicted value y ^ _k of data at a certain time k (m + 1≤k≤M) in time series data (^ is expressed above y in the equation). It is an expression expressed by using the actual value y _kl of the data of the time kl (1 ≦ l ≦ m) before the time in the time series data.

Α in Equation 5 is a coefficient of the autoregressive model. Further, m is an integer less than M indicating how many past data before that time are used to approximate y _k , which is the value of the transition data y corresponding to a certain time k in the autoregressive model. , In this experiment, it is set to 500.
Then, using the least squares method, a conditional expression for approximating the predicted value y ^ _k by the autoregressive model to the measured value y _k is obtained. As a condition for approximating the predicted value y ^ _k by the autoregressive model to the measured value y _k , consider minimizing the root-mean-squared error between y ^ _k and y _k given in Equation 5. That is, in this experiment, the least squares method is used to approximate the predicted value y ^ _k by the autoregressive model to y _k . The following equation 6 is a conditional equation for minimizing the square error between the transition data and the predicted value by the autoregressive model.

From Equation 6, the relationship of Equation 7 below is satisfied.

Further, by transforming the equation 7 (matrix notation), the following equation 8 is obtained.

R _jl in the equation 8 is called the autocorrelation of the transition data y, and is a value defined by the following equation 9. | Jl | at this time is called a time difference.

Based on Equation 8, consider Equation 10 which is a relational expression regarding the coefficients of the following autoregressive model. Equation 10 is an equation derived from the condition that minimizes the error between the predicted value of the transition data by the autoregressive model and the transition data at the time corresponding to the predicted value, and is the Yule-Walker equation. It is called. Equation 10 is a linear equation whose variable vector is a vector consisting of the coefficients of the autoregressive model, and the constant vector on the left side in Equation 10 is a vector whose component is the autocorrelation of transition data with a time difference of 1 to m. In the following, it will be an autocorrelation vector. Further, the coefficient matrix on the right side in Equation 10 is a matrix whose component is the autocorrelation of the transition data whose time difference is from 0 to m-1, and is referred to as an autocorrelation matrix below.

Further, the autocorrelation matrix (m × m matrix composed of R _jl ) on the right side in the equation 10 is referred to as an autocorrelation matrix R as in the following equation 11.

Generally, when obtaining the coefficient of the autoregressive model, a method of solving Equation 10 with respect to the coefficient α is used. In Equation 10, the coefficient α is derived so that the predicted value y ^ _k of the transition data at a certain time k derived by the autoregressive model is as close as possible to the actual value y _k of the transition data at that time k. Therefore, the frequency characteristics of the autoregressive model include a large number of frequency components included in the actual value y _k of the transition data at each time. Therefore, for example, when there is a lot of noise included in the transition data y, it is not possible to extract a signal related to the vibration of the bearing 106, or it is not possible to extract features according to the mode of failure of the bearing 106. Problems arise.
Therefore, the present inventors focused on the autocorrelation matrix R multiplied by the coefficient α of the autoregressive model, and as a result of diligent studies, used a part of the eigenvalues of the autocorrelation matrix R and included it in the transition data y. I came up with the idea that the autocorrelation matrix R should be rewritten so that the influence of noise is reduced and the signal components related to abnormalities (for example, flaws, stains, etc.) that occur in the bearing are emphasized (the SN ratio is increased).
A specific example of this will be described below.
The autocorrelation matrix R is decomposed into singular values. Since the components of the autocorrelation matrix R are symmetric, when the autocorrelation matrix R is decomposed into singular values, the product of the orthogonal matrix U, the diagonal matrix Σ, and the transposed matrix of the orthogonal matrix U is shown in Equation 12 below. It becomes.

As shown in Equation 13, the matrix Σ of the equation 12 is a diagonal matrix in which the diagonal component is an eigenvalue of the autocorrelation matrix R. Let the diagonal components of the diagonal matrix Σ be σ ₁₁ , σ ₂₂ , ..., Σ _mm . Further, the matrix U is an orthogonal matrix in which each column component vector is an eigenvector of the autocorrelation matrix R. Let the column component vector of the orthogonal matrix U be u ₁ , u ₂ , ..., U _m . There is a correspondence that the eigenvalue of the autocorrelation matrix R with respect to the _eigenvector u _j is σ j j. The eigenvalue of the autocorrelation matrix R is a variable that reflects the intensity of the component of each frequency included in the time waveform of the predicted value of the transition data by the autoregressive model.

FIG. 3 is a diagram showing the distribution of the eigenvalues of the autocorrelation matrix R obtained in the above procedure for the transition data obtained from the measurement data measured when the bearing 106 has a bearing with a flaw in the outer ring. ..
The graph of FIG. 3 is a graph in which the eigenvalues σ ₁₁ to σ _mm obtained by singular value decomposition of the autocorrelation matrix R are sorted and plotted in ascending order. Is shown.
Looking at FIG. 3, it can be seen that there is one eigenvalue with a significantly higher value than the others. Also, looking at the values of the other eigenvalues, it can be seen that the two eigenvalues have relatively higher values than the other eigenvalues.

Further, the distribution of the eigenvalues of the autocorrelation matrix R obtained by the above procedure for the transition data obtained from the measurement data measured when the bearing 106 is a normal bearing without defects is the same as in FIG. In addition, there is one eigenvalue that has a significantly higher value than the others, and among the other eigenvalues, some eigenvalues have a relatively higher value than the others.
In any case, it can be seen that the number of eigenvalues whose values are significantly higher than the others among the eigenvalues of the autocorrelation matrix R is significantly smaller than the total number of eigenvalues. Therefore, it can be determined that the number of eigenvalues that are significantly smaller than the total number of eigenvalues and the eigenvalues that are significantly higher than the others are the eigenvalues corresponding to the dominant component of the autocorrelation matrix R. The dominant component of a matrix is the component that makes up the majority of the matrix. Therefore, the inventors dominate by modifying the autocorrelation matrix R (generating the matrix R') using only the dominant eigenvalues among all the eigenvalues and not using the other eigenvalues. I got the idea that it is possible to exclude unnecessary components such as noise while leaving the components. The dominant eigenvalues of a matrix are the eigenvalues corresponding to the dominant components of the matrix.

Therefore, after finding the eigenvalues σ ₁₁ , σ ₂₂ , ···, σ _mm of the matrix R, the dominant eigenvalues among σ ₁₁ , σ ₂₂ , ···, σ _mm were determined.
In this experiment, the averages of all σ ₁₁ , σ ₂₂ , ..., Σ _mm were calculated, and all the eigenvalues larger than the calculated averages were determined as the dominant eigenvalues. In this experiment, the three eigenvalues of σ ₁₁ , σ ₂₂ , and σ ₃₃ are the dominant eigenvalues in both the case of using a normal bearing 106 without flaws and the case of using a bearing 106 with flaws in the outer ring. Was decided as. That is, the value of the number of eigenvalues s used, which is the number of eigenvalues used, is 3.
The dominant eigenvalues can also be determined as follows. For example, select the eigenvalues selected from the larger ones so that the ratio of the total of the selected eigenvalues to the total of σ ₁₁ , σ ₂₂ , ..., Σ _mm is equal to or more than a predetermined threshold (for example, 95%). , Can be determined as the dominant eigenvalue. Also, a predetermined threshold selected so that the ratio of the total of the selected eigenvalues to the total of σ ₁₁ , σ ₂₂ , ..., Σ _mm is equal to or higher than a predetermined threshold (for example, 75%). (For example, 1, 3, 5, 1% of the total number of eigenvalues, etc.) The following eigenvalues can be determined as the dominant eigenvalues.
The values of σ ₁₁ , σ ₂₂ , ..., σ _mm , which are the diagonal components of the diagonal matrix Σ obtained as a result of the singular value decomposition of the autocorrelation matrix R, are in descending order to simplify the notation of the formula. .. Of these eigenvalues of the autocorrelation matrix R, s eigenvalues determined as dominant eigenvalues are used to define the matrix R'as in Equation 14 below. The matrix R'is a matrix obtained by approximating the autocorrelation matrix R by using s eigenvalues of the eigenvalues of the autocorrelation matrix R.

The matrix Us in Eq. 14 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 Eq. 12. That is, the matrix Us is a submatrix formed by cutting out the component of m × _s on the left from the orthogonal matrix U. Further, Us ^T 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 of the equation 12. The matrix Σ _s in the equation 14 is an s × s matrix composed of s columns from the left and s rows from the top of the diagonal matrix Σ of the equation 12. That is, the matrix Σ _s is a submatrix formed by cutting out the component of s × s on the upper left from the diagonal matrix Σ.
If the matrix Σ _s and the matrix _Us are expressed as matrix components, the following equation 15 is obtained.

By using the matrix R'instead of the autocorrelation matrix R, the relational expression of the equation 10 is rewritten as the following equation 16.

By modifying the equation 16, the equation 17 for obtaining the coefficient α can be obtained. A model for calculating the predicted value y ^ _k by the equation 5 using the coefficient α obtained by the equation 17 is referred to as a “modified autoregressive model”.
So far, the values of σ ₁₁ , σ ₂₂ , ..., σ _mm , which are the diagonal components of the diagonal matrix Σ, have been described in descending order, but in the process of calculating the coefficient α, the diagonal components of the diagonal matrix Σ are in descending order. It does not have to be, in which case the matrix Us is constructed by cutting out the column component vector (unique vector) corresponding to the eigenvalues used, rather than cutting out the left m × _s component from the orthogonal matrix U. It is a partial matrix, and the matrix Σ _s is a partial matrix that is not cut out from the diagonal matrix Σ but the component of s × s on the upper left, but is cut out so that the eigenvalue used is the diagonal component.
Equation 17 is an equation used to determine the coefficients of the modified autoregressive model. The matrix Us of Eq. 17 is a _submatrix of the orthogonal matrix obtained by the singular value decomposition of the autocorrelation matrix R, and is a matrix whose column component vector is the eigenvector corresponding to the eigenvalue to be used. This is just one example. Further, the matrix Σ _s of the equation 17 is an example of a second matrix which is a submatrix of the diagonal matrix obtained by the singular value decomposition of the autocorrelation matrix R and whose diagonal component is the eigenvalues used. Is. The matrix _Us Σ _{s Us} ^T in Equation 17 is an example of the first matrix which is a matrix derived from the matrix Σ _s and the matrix _Us .

By calculating the right side of Eq. 17, the coefficient α of the modified autoregressive model can be obtained. The above is an example of how to derive the coefficients of the modified autoregressive model, but for the derivation of the coefficients of the underlying autoregressive model, the least squares method is used for the predicted values so that it is intuitively easy to understand. It was explained by the method used. However, in general, a method of defining an autoregressive model using the concept of a stochastic process and deriving its coefficient is known. In that case, the autocorrelation is expressed by the autocorrelation of the stochastic process (population), and the autocorrelation of this stochastic process is expressed as a function of the time difference. Therefore, the autocorrelation of the measurement data in the present 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, the time difference is 0 for R ₂₂ to R _mm . Although it is an autocorrelation of, these may be replaced with R ₁₁ .
Next, the predicted value of the transition data is obtained by the modified autoregressive model specified by the obtained coefficient α, and the predicted value of the transition data is subjected to Fourier transform on the data consisting of the predicted value of the transition data. Obtain the power spectrum of the data consisting of.

In this experiment, the autocorrelation matrix R is obtained for each of the obtained transition data using the equations 9 and 11, and the eigenvalues of the autocorrelation matrix R are obtained by performing the singular value decomposition represented by the equation 12. The distribution of the eigenvalues of the correlation matrix R was obtained. In addition, the waveform of the transition data was obtained for each of the obtained transition data. Further, for each of the obtained transition data, the matrix Σ _s and the matrix _Us are obtained from the singular value decomposition of the autocorrelation matrix R obtained in the above procedure using the equation 15, and corrected using the equations 9 and 17. The coefficient α of the obtained autoregressive model was obtained, and the waveform of the modified autoregressive model specified by the obtained coefficient α was obtained. Then, the power spectrum of this waveform was obtained by performing a Fourier transform on the obtained modified autoregressive model waveform for each of the obtained transition data.
Further, as a comparison target, when a normal bearing 106 without defects is used and when a bearing 106 with defects is used for the outer ring, each of them can be obtained from the analysis signal v _a of the measurement data v using Equation 3. The power spectrum of the transition data y was obtained by performing a Fourier transform on each of the transition data y (environment).
Further, as a comparison target, when a normal bearing 106 without defects is used and when a bearing 106 with defects is used for the outer ring, each of them can be obtained from the analysis signal v _a of the measurement data v using Equation 3. By applying a Fourier transform to the signal obtained by applying a low-pass filter to the transition data y (envelope), the power spectrum of the signal obtained by applying this low-pass filter was obtained. Here, the power is applied to the transition data y when a low-pass filter with a cutoff frequency of 1500 Hz is applied, when a low-pass filter with a cutoff frequency of 800 Hz is applied, and when a low-pass filter with a cutoff frequency of 600 Hz is applied. The spectrum was calculated.

The obtained experimental results will be described with reference to FIGS. 4 to 9.
FIG. 4 is a diagram showing measurement data v measured for each of the case where the normal bearing 106 without flaws is used and the bearing 106 with flaws is used for the outer ring.
The graph of FIG. 4A shows the waveform of the measurement data v measured when the normal bearing 106 without defects is used. The horizontal axis of the graph of FIG. 4A shows time, and the vertical axis shows amplitude. The graph of FIG. 4B shows the waveform of the measurement data v measured when the bearing 106 having a flaw in the outer ring is used. The horizontal axis of the graph of FIG. 4B shows time, and the vertical axis shows amplitude.
Looking at the graph of FIG. 4 (a) and the graph of FIG. 4 (b), they have similar waveforms. Therefore, it is difficult to diagnose whether the bearing 106 is normal or abnormal from these waveforms.

FIG. 5 is a diagram showing a power spectrum of transition data y obtained from the analysis signal v _a of the measurement data v using the equation 3 when a normal bearing 106 without defects is used. The power spectrum of FIG. 5 is a power spectrum showing the power of a signal having a frequency from 0 Hz to 1600 Hz. The horizontal axis of the power spectrum indicates the frequency, and the vertical axis indicates the signal intensity of the corresponding frequency.
FIG. 6 shows the predicted value of the transition data obtained by the modified autoregressive model specified by the coefficient α obtained in the above procedure from the transition data y obtained when the normal bearing 106 without defects is used. It is a figure which shows the power spectrum about the data which consists of. The power spectrum of FIG. 6 is a power spectrum showing the power of a signal having a frequency from 0 Hz to 1600 Hz.
Looking at the power spectra of FIGS. 5 and 6, it can be seen that in the power spectrum of FIG. 6, the signal having a frequency of about 800 Hz or higher is significantly attenuated as compared with the power spectrum of FIG. The power spectrum of FIG. 6 is a power spectrum of a modified autoregressive model obtained by using only the dominant autocorrelation matrix eigenvalues for the transition data y. Therefore, it can be determined that the essential component of the transition data y is a signal of 0 Hz to about 800 Hz. Therefore, when some abnormality occurs in the bearing 106 and the transition data y is affected by the abnormality, the influence is a signal (corrected autoregressive model) of 0 Hz to about 800 Hz, which is an essential component in the transition data y. It can be judged that it appears in the essential component of).

FIG. 7 is a diagram showing a power spectrum of transition data y obtained from the analysis signal v _a of the measurement data v using the equation 3 when the bearing 106 having a flaw in the outer ring is used. The power spectrum of FIG. 7A is a power spectrum showing the power of a signal having a frequency from 0 Hz to 40,000 Hz. The power spectrum of FIG. 7 (b) is a power spectrum showing the power of a signal having a frequency from 0 Hz to 18000 Hz, and is a power spectrum obtained by enlarging a part of the power spectrum of FIG. 7 (a). The power spectrum of FIG. 7 (c) is a power spectrum showing the power of a signal having a frequency from 0 Hz to 1600 Hz, and is a power spectrum obtained by enlarging a part of the power spectrum of FIG. 7 (a).
FIG. 8 shows the predicted value of the transition data obtained by the modified autoregressive model specified by the coefficient α obtained in the above procedure from the transition data y obtained when the bearing 106 having a flaw in the outer ring is used. It is a figure which shows the power spectrum about the data which consists of. The power spectrum of FIG. 8A is a power spectrum showing the power of a signal having a frequency from 0 Hz to 40,000 Hz. The power spectrum of FIG. 8 (b) is a power spectrum showing the power of a signal having a frequency from 0 Hz to 1600 Hz, and is a power spectrum obtained by enlarging a part of the power spectrum of FIG. 8 (a).

Looking at the power spectrum in FIG. 7 (c), peaks were seen near 260 Hz, around 520 Hz, which is twice the frequency, and around 780 Hz, which is three times the frequency, and the flaws on the outer ring of the bearing 106. You can see that the corresponding signal is coming out. However, looking at the power spectrum of FIG. 7B, it is similar to the peak seen in the range of 0 Hz to about 800 Hz at frequencies above the range of 0 Hz to about 800 Hz, which is judged to be an essential component of the transition data y. It can be seen that there are many peaks of the intensity of. Further, looking at the power spectrum of FIG. 7 (a), it can be seen that many peaks are present even at the frequency (18000 Hz) or higher shown in FIG. 7 (b). Depending on the type of flaw, a peak may occur in the range of 18000 Hz or higher, so when diagnosing an abnormality in the bearing 106 based on the power spectrum of the transition data y, the abnormality may be over-detected. ..
Comparing the power spectrum of FIG. 8 (b) with the power spectrum of FIG. 6, the power spectrum of FIG. 8 (b) is around 260 Hz, which is a frequency corresponding to the rotation cycle of the flaw in the outer ring of the bearing 106. It can be seen that the peak stands at around 520 Hz, which is twice that. That is, in the power spectrum of FIG. 8B, a peak corresponding to the rotation frequency related to the flaw in the outer ring of the bearing 106 is generated.
Looking at the power spectrum of FIG. 8A and the power spectra of FIGS. 7A and 7B, the components of the power spectrum of FIG. 8A having a frequency of 800 Hz or higher are shown in FIG. 7 (a). It can be seen that the power spectra of a) and (b) are significantly attenuated. Therefore, the inventors over-detect the abnormality by diagnosing the abnormality of the bearing 106 based on the power spectrum of FIG. 8 as compared with the case of diagnosing the abnormality of the bearing 106 based on the power spectrum of FIG. I got the knowledge that it is possible to prevent such a situation.

FIG. 9 is a diagram showing a power spectrum of the transition data y obtained when the bearing 106 having a flaw in the outer ring is applied and the data obtained by applying a low-pass filter.
The power spectrum of FIG. 9A is a power spectrum of transition data y subjected to a low-pass filter designed to cut frequencies of 1500 Hz or higher. The power spectrum of FIG. 9B is a power spectrum of transition data y subjected to a low-pass filter designed to cut frequencies of 800 Hz or higher. The power spectrum of FIG. 9C is a power spectrum of transition data y subjected to a low-pass filter designed to cut frequencies of 600 Hz or higher.
Looking at the power spectrum of FIG. 9A, there are significantly higher peaks at around 260 Hz and around 520 Hz than other peaks, and a signal corresponding to a flaw in the outer ring of the bearing 106 is output. I understand that.

Looking at the power spectrum of FIG. 9B, it can be seen that there is a significantly higher peak than the other peaks in the vicinity of 260 Hz. However, the peak near 520 Hz is about the same as the peak seen near 0 Hz to 200 Hz, and the difference from the peak seen near 0 Hz to 200 Hz is not clear, so the peak near 520 Hz is not detected. There is a possibility that it will become.
Looking at the power spectrum of FIG. 9 (c), it can be seen that there is a significantly higher peak than the other peaks in the vicinity of 260 Hz. However, the peak near 520 Hz is lower than the peak seen near 0 Hz to 200 Hz, and the peak near 520 Hz is not detected as an unimportant peak smaller than the peak seen near 0 Hz to 200 Hz. There is a possibility that it will become.
Since the signal peak corresponding to the flaw in the outer ring of the bearing 106 can be seen in the power spectrum of FIG. 9 (a), the bearing 106 can be appropriately diagnosed based on the power spectrum of FIG. 9 (a). can. However, in the power spectra of FIGS. 9B and 9C, the peak near 520 Hz among the peaks of the signal corresponding to the flaw in the outer ring of the bearing 106 may not be detected. Therefore, the bearing 106 is diagnosed. It may not be possible to do it properly.

As described above, it was confirmed that when the low-pass filter is used, the signal of the component important for diagnosis may be attenuated depending on the frequency to be cut, so that the signal may not be detected. In addition, which frequency should be designed to cut the low-pass filter must be determined by the user's experience. Therefore, it is difficult to design a low-pass filter to cut an appropriate frequency.
On the other hand, in the method performed in this experiment, the transition data y is acquired from the measurement data v, and the transition is used by using the dominant eigenvalue quantitatively selected from the eigenvalues of the autocorrelation matrix R of the acquired transition data y. The coefficient α of the modified autoregressive model of the data y was obtained, and the diagnosis was performed based on the obtained coefficient α. As described above, since the method performed in this experiment does not require the user to determine the parameters by qualitative judgment, it is possible to prevent a situation in which the quality of diagnosis is deteriorated by the user's judgment. Looking at the power spectrum of FIG. 8B, the autoregressive model specified by the coefficient α determined by using the dominant eigenvalue quantitatively selected from the eigenvalues of the autocorrelation matrix R is used. It can be seen that the signals important for diagnosis (signals corresponding to the peaks around 260 Hz and around 520 Hz) are maintained.

As described above, the present inventors obtain the coefficient α of the modified autoregressive model of the transition data y by using only the dominant eigenvalue among the eigenvalues of the autocorrelation matrix R of the transition data y. It was possible to obtain the finding that it is possible to obtain data obtained by extracting a component useful for diagnosing an abnormality of an object from the components contained in the data y.
The process of this embodiment is as follows. That is, based on the findings obtained in this experiment, the autocorrelation matrix R obtained from the transition data showing the temporal transition of the amplitude of the measurement data of the vibration of the object is decomposed into singular values, and among the eigenvalues obtained. The dominant eigenvalues of are used to determine the coefficients of the modified autoregressive model that approximates the transition data. Next, from the modified autoregressive model specified by the obtained coefficient, the calculation on the right side of Equation 5 is performed to obtain the predicted value of the transition data, and the data consisting of the predicted value of the transition data is subjected to the Fourier transform. By doing so, the power spectrum of the data consisting of the predicted values of this transition data is acquired. Then, it is a process of diagnosing an abnormality of an object based on the acquired power spectrum.

(System configuration)
FIG. 10 is a diagram showing an example of the system configuration of the diagnostic system of the present embodiment. The diagnostic system is a system for diagnosing abnormalities in an object that moves periodically. The diagnostic system includes an information processing device 1000 and a vibration measuring device 1001. In the present embodiment, the diagnostic system performs abnormality diagnosis of bearings used in railway bogies.
The information processing device 1000 is an information processing device such as a personal computer (PC), a server device, a tablet device, or the like that performs abnormality diagnosis of bearings based on a signal measured by the vibration measuring device 1001. Further, the information processing apparatus 1000 may be a computer or the like built in a train.
The vibration measuring device 1001 includes a sensor such as an acceleration sensor, detects the vibration of an object via the sensor, and outputs a signal corresponding to the detected vibration to an external device such as the information processing device 1000 by wire or wirelessly. It is a device.

(Functional configuration of information processing equipment)
An example of the function of the information processing apparatus 1000 will be described with reference to FIG.
The information processing apparatus 1000 includes an acquisition unit 1010, a determination unit 1020, a diagnosis unit 1030, and an output unit 1040.
≪Acquisition part 1010≫
The acquisition unit 1010 acquires the measurement data v related to the periodic motion of the object that performs the periodic motion, and based on the acquired measurement data v, shows the state of the temporal transition of the amplitude in the measurement data v. The transition data y shown is acquired.
In the present embodiment, the acquisition unit 1010 rotates the small gear shaft 100, acquires the vibration measurement data v measured by the vibration measurement device 1001 installed at the position 111, and based on the acquired measurement data v, obtains the vibration measurement data v. The transition data y showing the temporal transition of the amplitude in the measurement data is acquired.

≪Decision part 1020≫
The determination unit 1020 determines the coefficient α in the modified autoregressive model based on the transition data y acquired by the acquisition unit 1010. The modified autoregressive model uses the actual value y _k-1 to y _km of the transition data y and the coefficient α (= α ₁ to α _m ) for this actual value, and the predicted value y of the transition data y. It is an equation 5 expressing ^ _k . The determination unit 1020 determines a dominant eigenvalue from the eigenvalues of the autocorrelation matrix R represented by the equation 11 obtained from the transition data y, and is essentially from the autocorrelation matrix R based on the determined dominant eigenvalues. The matrix R'represented by the equation 14 from which the components are extracted is generated. The matrix R'is an example of the first matrix. The determination unit 1020 uses the coefficient α in the modified autoregressive model to determine the coefficient in a generally known autoregressive model in equation 10 (Yur-Walker equation), which is represented by equation 11. Instead of the matrix R, the equation 16 which is an equation using the generated matrix R'(Equation 14) is used for determination. In Equation 10, the autocorrelation matrix R whose component is the autocorrelation of the transition data y whose time difference is from 0 to m-1 is a coefficient matrix, and the autocorrelation of the transition data y whose time difference is from 1 to m is a component. It is an equation whose correlation vector is a constant vector.
Equation 10 minimizes the square error between the predicted value y ^ _k of the transition data y calculated by the equation 5 and the measured value y _k of the transition data y at the time k corresponding to the predicted value y ^ _k of the transition data y. It can be derived as a conditional expression indicating the conditions to be converted. The matrix R'has a diagonal matrix Σ whose diagonal component is the eigenvalue of the autocorrelation matrix R derived by singular value decomposition of the autocorrelation matrix R (Equation 12) and a column component of the eigenvector of the autocorrelation matrix R. It is derived from the orthogonal matrix U and. The matrix R'is a submatrix of the diagonal matrix Σ using s eigenvalues determined as the dominant eigenvalues among the eigenvalues of the autocorrelation matrix R, and the s eigenvalues are diagonal components. It is a matrix _Us Σ _{s Us} ^T derived from a matrix Σ _s and a matrix Us which is a submatrix of the orthogonal matrix U and whose eigenvectors corresponding to _s eigenvalues are column component vectors.

≪Diagnosis Department 1030≫
The diagnosis unit 1030 diagnoses an abnormality of the object based on the coefficient α determined by the determination unit 1020. The diagnostic unit 1030 obtains the predicted value of the transition data from the modified autoregressive model specified by the coefficient α determined by the determination unit 1020, and performs a Fourier transform on the data consisting of the predicted value of the transition data. Then, the power spectrum of the data consisting of the predicted values of the transition data may be obtained, and the abnormality of the object may be diagnosed based on this power spectrum. Further, the diagnosis unit 1030 may determine the presence or absence of an abnormality in the object as a result of the diagnosis based on the frequency indicating the peak in the power spectrum, or may use the portion having the abnormality in the object as the result of the diagnosis.
In the present embodiment, the presence or absence of a flaw in the bearing 106 is the result of the diagnosis.
<< Output section 1040 >>
The output unit 1040 outputs information related to the result of the diagnosis by the diagnosis unit 1030.

(Hardware configuration of information processing equipment)
FIG. 11 is a diagram showing an example of the hardware configuration of the information processing apparatus 1000.
The information processing device 1000 includes a CPU 1100, a main storage device 1101, an auxiliary storage device 1102, and an input / output I / F 1103. The components are communicably connected to each other via the system bus 1104.
The CPU 1100 is a central arithmetic unit that controls the information processing device 1000. The main storage device 1101 is a storage device such as a RAM (Random Access Memory) that functions as a work area of the CPU 1100 or a temporary storage place for data. The auxiliary storage device 1102 includes a ROM (Read Only Memory), an HDD (Hard Disk Drive), and an SSD (Solid State Drive) that store various programs, setting data, measurement data output from the vibration measurement device 1001, diagnostic information, and the like. Etc. storage device. The input / output I / F 1103 is an interface used for exchanging information with an external device such as the vibration measuring device 1001.
When the CPU 1100 executes processing based on a program stored in the auxiliary storage device 1102 or the like, the functions of the information processing apparatus 1000 described with reference to FIG. 10 and the processing of the flowchart described later with reference to FIG. 12 are realized.

(Abnormal diagnosis processing)
In the present embodiment, the diagnostic system shows the temporal transition of the amplitude of the measurement data based on the vibration measurement data measured by the vibration measurement device 1001 installed at the position 111 in the same situation as in FIG. The transition data is acquired, and the abnormality of the bearing 106 is diagnosed based on the acquired transition data. In the present embodiment, the diagnostic system diagnoses the abnormality of the bearing 106 by identifying whether or not the bearing 106 has a defect. In the present embodiment, the diagnostic system diagnoses the abnormality of the bearing 106 based on the measurement data measured in advance by the vibration measuring device 1001.
FIG. 12 is a flowchart showing an example of processing of the information processing apparatus 1000.
In S1201, the acquisition unit 1010 acquires v ₁ to v _M , which are measurement data from time 1 to M, as vibration measurement data v measured by the vibration measuring device 1001. Then, the acquisition unit 1010 acquires the analysis signal v _a from the acquired measurement data v by a method using the Fourier transform using the equation 4. The acquisition unit 1010 acquires the envelope of the measurement data v as the transition data y using the equation 3 based on the analysis signal v _a . The acquisition unit 1010 acquires y ₁ to y _M , which are transition data from time 1 to M, as transition data y.
Further, the acquisition unit 1010 obtains, for example, a function v'(t) = | v (t) | obtained by multiplying a portion having a negative value in v (t) by -1 to obtain a positive value. 'For (t), a signal obtained by applying a low-pass filter that cuts a signal having a frequency equal to or higher than a predetermined threshold value may be acquired as transition data y. Further, the acquisition unit 1010 identifies the mountain portion in the function v'(t) and acquires the signal indicated by the function obtained by interpolating the specified portion (for example, polynomial interpolation) as the transition data y. May be good.

In S1202, the determination unit 1020 indicates the transition data y acquired in S1201, the preset constant M, and the number of past data to approximate the data at a certain time in the modified autoregressive model. Based on m, an autocorrelation matrix R is generated using equations 9 and 11. The determination unit 1020 acquires M and m by reading out the information of M and m stored in advance. In this embodiment, the value of m is 500. Further, M is an integer larger than m.
In S1203, the determination unit 1020 obtains the orthogonal matrix U and the diagonal matrix Σ of the equation 12 by singular value decomposition of the autocorrelation matrix R generated in S1202, and the eigenvalues of the autocorrelation matrix R from the diagonal matrix Σ. Obtain σ ₁₁ to σ _mm .

In S1204, the determination unit 1020 determines the dominant eigenvalue among the eigenvalues of the autocorrelation matrix R. For example, the determination unit 1020 obtains the average value of all the eigenvalues of the matrix R, identifies all the eigenvalues larger than the obtained mean value among the eigenvalues of the matrix R, and determines the specified eigenvalue as the dominant eigenvalue. .. Then, the determination unit 1020 determines the number of eigenvalues used s to be the number of eigenvalues selected as the dominant eigenvalues.
Further, the determination unit 1020 is set so that, for example, the ratio of the total of the selected eigenvalues to the total of σ ₁₁ , σ ₂₂ , ..., Σ _mm is equal to or higher than a predetermined threshold value (for example, 95%). , The eigenvalues may be selected (eg, select from the one with the largest value) and the selected eigenvalues may be determined as the dominant eigenvalues. Further, the determination unit 1020 sets the ratio of the total of the selected eigenvalues to the total of σ ₁₁ , σ ₂₂ , ..., Σ _mm to be equal to or higher than a predetermined threshold value (for example, 75%). A number of eigenvalues equal to or less than a predetermined threshold (for example, one, three, five, 1% of the total number of eigenvalues, etc.) may be selected, and the selected eigenvalues may be determined as the dominant eigenvalues. ..

In S1205, the determination unit 1020 is based on the measurement data y, the dominant eigenvalues σ ₁₁ to σ _ss determined in S1204, and the orthogonal matrix U obtained by the singular value decomposition of the autocorrelation matrix R. 17 is used to determine the coefficient α of the modified autoregressive model.
In S1206, the diagnostic unit 1030 obtains the predicted value of the transition data from the modified autoregressive model specified by the coefficient α determined in S1205, and performs a Fourier transform on the data consisting of the predicted value of the transition data. Then, the power spectrum of the data consisting of the predicted values of this transition data is acquired.

In S1207, the diagnostic unit 1030 diagnoses the abnormality of the bearing 106 based on the power spectrum acquired in S1206.
In the present embodiment, the diagnostic unit 1030 specifies, for example, a frequency corresponding to a signal indicating an intensity equal to or higher than a predetermined threshold value in the power spectrum acquired in S1206. Then, the diagnostic unit 1030 determines whether or not a frequency that is an integral multiple of another frequency exists in the specified frequency. For example, the diagnostic unit 1030 selects one by one from the specified frequencies in order, and for each selected frequency, the selected frequency is multiplied by an integer (for example, doubled), and the specified frequency is included in the specified frequency. Get the difference between each value of the frequency of. Then, if the acquired difference is equal to or less than a predetermined threshold value (for example, 1, 5, etc.), the diagnostic unit 1030 is an integral multiple of the other frequency in the specified frequency. It is determined that the frequency is present, and it is diagnosed that the bearing 106 is defective.
Further, the diagnostic unit 1030 determines that there is no frequency that is an integral multiple of the other frequencies in the specified frequency if the acquired difference does not exceed a predetermined threshold value. It is diagnosed that the bearing 106 is in an unknown state.
Further, when the frequency corresponding to the signal indicating the intensity equal to or higher than the threshold value does not exist, the diagnosis unit 1030 diagnoses that the bearing 106 is normal without any abnormality.
In S1208, the output unit 1040 outputs information indicating the result of the diagnosis of the abnormality of the bearing 106. The output unit 1040 outputs, for example, by displaying information indicating the result of the diagnosis of the abnormality of the bearing 106 on the display device. Further, the output unit 1040 may output, for example, by storing information indicating the result of the diagnosis of the abnormality of the bearing 106 in the auxiliary storage device 1102. Further, the output unit 1040 may output by transmitting information indicating the result of the diagnosis of the abnormality of the bearing 106 to a set destination such as an external server device.

(summary)
As described above, in the present embodiment, the diagnostic system acquires transition data showing the temporal transition of the amplitude of the measurement data based on the measurement data measured from the periodic motion of the object, and the acquired transition data. Therefore, the autocorrelation matrix R was generated, the autocorrelation matrix R was decomposed into singular values, and the eigenvalues that were quantitatively dominant were determined from the obtained eigenvalues. The diagnostic system then used the determined dominant eigenvalues to determine the coefficient α of the modified autoregressive model that approximates the transitional data. Then, the diagnostic system obtains the predicted value of the transition data by the modified autoregressive model specified by the determined coefficient α, obtains the power spectrum of the data consisting of the predicted value of the transition data, and is based on the obtained power spectrum. The abnormality of the bearing 106 was diagnosed. The diagnostic system has been modified to approximate the transition data so that by using some of the eigenvalues of the autocorrelation matrix R, useful components remain for abnormal diagnosis of the bearing 106 and no unhelpful components remain. The coefficient α of the autoregressive model can be determined. As a result, the diagnostic system can perform the abnormality diagnosis more accurately based on the components useful for the abnormality diagnosis of the bearing 106 of the transition data.
Further, by the processing of the present embodiment, the diagnostic system does not need to qualitatively determine the frequency to be cut as in the case of using the low-pass filter, so that a signal important for diagnosis is obtained as in the case of using the low-pass filter. It is possible to prevent a situation in which the attenuation is undetectable.
Further, by the processing of the present embodiment, the diagnostic system can extract components useful for abnormality diagnosis from the transition data without needing to assume in advance what frequency the signal used for abnormality diagnosis is. ..

In the present embodiment, the diagnostic system is to perform an abnormality diagnosis of the bearing of the railroad bogie. However, the diagnostic system may perform abnormality diagnosis on a rotating body such as a gear, a vibrating body such as a vibrator, an elastic body such as a spring, and other objects that perform periodic movements such as the heart of an organism.
In this embodiment, m is a preset number of 500. However, the number of past data that can be appropriately approximated to the measured data may be specified by conducting an experiment according to the diagnosis target, and the specified number may be used as the value of m. For example, the information processing apparatus 1000 uses a self-regressive model or the like for the transition data obtained from the measurement data measured from the diagnosis target by using the transition data at a certain time and the transition data past the time. The number of past transition data used for the approximation when the difference between the approximated value and the transition data at that time is less than the set threshold value may be determined as m.
In the present embodiment, the diagnostic system is determined to diagnose the abnormality of the bearing 106 based on the measurement data measured in advance by the vibration measuring device 1001. However, the diagnostic system may diagnose the abnormality of the bearing 106 in operation by using the measurement data that is continuously measured and output by the vibration measuring device 1001 in real time. That is, every time new measurement data v is acquired from the vibration measurement device 1001, the information processing apparatus 1000 updates the transition data y ₁ to y _M from the acquired measurement data v and performs the processing of FIG. You may do it.
In the present embodiment, the information processing apparatus 1000 realizes the process of FIG. 12 by executing the program stored in the auxiliary storage apparatus 1102. However, the information processing apparatus 1000 may realize the process of FIG. 12 by executing a program stored in an external storage medium, an external storage server, or the like.
Further, for example, a part or all of the functions of the information processing apparatus 1000 described above may be mounted on the information processing apparatus 1000 as hardware.
In addition, the embodiments of the present invention described above are merely examples of embodiment of the present invention, and the technical scope of the present invention should not be construed in a limited manner by these. It is a thing. That is, the present invention can be implemented in various forms without departing from the technical idea or its main features.

1000 Information processing device 1010 Acquisition unit 1020 Determination unit 1030 Diagnosis unit 1040 Output unit 1001 Vibration measurement device 1100 CPU

Claims (11)

An acquisition means for acquiring transition data showing the state of temporal transition of the amplitude of the measurement data based on the measurement data related to the periodic motion of the object performing the periodic motion.
A determination means for determining the coefficient in the modified autoregressive model based on the transition data acquired by the acquisition means, and a determination means.
A diagnostic means for diagnosing an abnormality of the object based on the coefficient determined by the determination means, and a diagnostic means.
Have,
The modified autoregressive model is an expression representing a predicted value of the transition data using the actual value of the transition data and the coefficient with respect to the actual value.
The determination means is a column of a diagonal matrix whose diagonal component is the eigenvalue of the autocorrelation matrix derived by singular value decomposition of the autocorrelation matrix derived from the transition data, and an eigenvector of the autocorrelation matrix. The coefficient is determined using an equation in which the orthogonal matrix as a component and the first matrix derived from the coefficient matrix are used and the eigenvalue vector derived from the transition data is a constant vector.
The autocorrelation vector is a vector whose component is the autocorrelation of the transition data from 1 to m, which is the number of the actual values used in the modified autoregressive model.
The autocorrelation matrix is a matrix whose component is the autocorrelation of the transition data having a time difference of 0 to m-1.
The first matrix includes s eigenvalues determined as dominant eigenvalues among the eigenvalues of the autocorrelation matrix, a second matrix Σ _s derived from the diagonal matrix, and s eigenvalues. And the third matrix _Us derived from the orthogonal matrix, and the matrix _Us Σ _{s Us} ^T derived from.
The second matrix is a submatrix of the diagonal matrix, and is a matrix having the s eigenvalues as diagonal components.
The third matrix is a submatrix of the orthogonal matrix, and is an information processing apparatus in which the eigenvectors corresponding to the s eigenvalues are used as column component vectors. The information processing apparatus according to claim 1, wherein the acquisition means acquires the envelope data of the measurement data as the transition data based on the measurement data. The information processing apparatus according to claim 1 or 2, wherein the s eigenvalues are eigenvalues larger than the average value of all the eigenvalues of the autocorrelation matrix among the autocorrelation matrices. The s eigenvalues are a number of eigenvalues equal to or less than a predetermined threshold value.
The information processing apparatus according to claim 1 or 2, wherein the ratio of the total of the s eigenvalues to the total of the total eigenvalues of the autocorrelation matrix is equal to or less than a predetermined threshold value. The autocorrelation matrix is a matrix included in a conditional expression showing a condition for minimizing the square error between the predicted value of the transition data and the measured value of the transition data at the time corresponding to the predicted value of the transition data. Item 4. The information processing apparatus according to any one of Items 1 to 4. The diagnostic means derives a power spectrum of data consisting of predicted values of the transition data obtained by the modified autoregressive model, and diagnoses an abnormality of the object based on the power spectrum, claims 1 to 5. The information processing device according to any one of the items. The information processing apparatus according to any one of claims 1 to 6, wherein the measurement data is measurement data related to vibration of the object. The information processing apparatus according to any one of claims 1 to 7, further comprising an output means for outputting information related to the result of diagnosis by the diagnostic means. The object is a bearing used for a railroad bogie.
The information processing apparatus according to any one of claims 1 to 8, wherein the diagnostic means diagnoses an abnormality including the presence of a flaw in the object based on the coefficient determined by the determination means. It is an information processing method executed by an information processing device.
Based on the measurement data related to the periodic motion of the object performing the periodic motion, the acquisition step of acquiring the transition data showing the state of the temporal transition of the amplitude of the measurement data, and the acquisition step.
A determination step that determines the coefficients in the modified autoregressive model based on the transition data acquired in the acquisition step, and
A diagnostic step for diagnosing an abnormality in the object based on the coefficient determined in the determination step,
Including
The modified autoregressive model is an expression representing a predicted value of the transition data using the actual value of the transition data and the coefficient with respect to the actual value.
In the determination step, a diagonal matrix having an eigenvalue of the autocorrelation matrix derived by singular value decomposition of the autocorrelation matrix derived from the transition data as a diagonal component and an eigenvector of the autocorrelation matrix are arranged. The coefficient is determined using an equation in which the orthogonal matrix as a component and the first matrix derived from the coefficient matrix are used and the eigenvalue vector derived from the transition data is a constant vector.
The autocorrelation vector is a vector whose component is the autocorrelation of the transition data from 1 to m, which is the number of the actual values used in the modified autoregressive model.
The autocorrelation matrix is a matrix whose component is the autocorrelation of the transition data having a time difference of 0 to m-1.
The first matrix includes s eigenvalues determined as dominant eigenvalues among the eigenvalues of the autocorrelation matrix, a second matrix Σ _s derived from the diagonal matrix, and s eigenvalues. And the third matrix _Us derived from the orthogonal matrix, and the matrix _Us Σ _{s Us} ^T derived from.
The second matrix is a submatrix of the diagonal matrix, and is a matrix having the s eigenvalues as diagonal components.
The third matrix is a submatrix of the orthogonal matrix, and is a matrix in which the eigenvectors corresponding to the s eigenvalues are used as column component vectors. A program for making a computer function as each means of the information processing apparatus according to any one of claims 1 to 9.

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