Measuring device, measurement system, measurement method, and measurement program

Abstract

To increase the rate of restoration of an original signal while reducing measurement data.SOLUTION: A measuring device includes a pre-processing unit 40 that pre-processes a signal to be measured a(t) that changes temporally, and a random measuring unit 1 that randomly measures a pre-processed signal s(t) pre-processed by the pre-processing unit 40 based on a first random matrix Φ. The pre-processing unit 40 down-samples the signal to be measured a(t) to a signal that is frequency-shifted downward by only a specific frequency. A measurement calculation apparatus includes a receiving unit 55 that receives a random measurement vector y that is a vector representation of a random measurement value measured at random from the random measuring unit 1, and an estimation unit 61 that estimates a coefficient x={xi} of an orthogonal basis matrix ψ as a regularization coefficient λ0 when the random measurement vector y is expressed as a product Φψx of a first random matrix Φ, an n×n orthogonal basis matrix ψ whose columns are a basis vector {Ψi}, and its coefficient x. A measurement system includes the measuring device and the measurement calculation apparatus.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a measuring device, a measurement system, a measurement method, and a measurement program, and more particularly, to a measuring device for evaluating the vibration of an ultrasonic horn, for example.

Background Art

[0002] Vibrating devices such as ultrasonic horns and rotating devices have resonance points depending on their materials and structures. Resonance characteristics are often evaluated by spectral distribution. In addition, these vibrating devices will inevitably fail due to material defects, fatigue, and aging. When a failure occurs, it will lead to equipment downtime and economic losses. Therefore, it is important to perform fault diagnosis on rotating equipment and keep it in a healthy state. Vibration evaluation and fault diagnosis of vibrating devices are performed by various sensing methods.

[0003] For example, Non-Patent Document 1 discloses a technique that combines compressive sensing technology and a method of measuring at a constant frequency with a random measurement start time (Random Start Uniform Sampling Method, hereinafter referred to as RSUSM). Compressive sensing theory is a technique that can accurately reconstruct a signal from much fewer measurement data than normally required if the measurement data has sparsity with respect to a certain basis (for example, Fourier basis) and the basis is incoherent (performing random sampling). Thus, the technique of Non-Patent Document 1 reduces the measurement data required for monitoring. In addition, Patent Document 1 discloses a measurement data providing service system that assigns an ID to a sensor, performs centralized management in a server system, and performs temperature compensation and linearity compensation processing according to the situation.

Prior Art Documents

Non-Patent Documents

[0004]

Non-Patent Document 1

Patent Document

[0005]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0006] The compressive sensing theory used in Non-Patent Document 1 requires that the measurement data be sparse with respect to the Fourier basis. However, the frequency spectrum may spread (i.e., the sparsity is low), and it may not be possible to restore the original signal with the required accuracy.

[0007] The present invention has been made in view of the above problems, and an object thereof is to provide a measuring device, a measurement system, a measurement method, and a measurement program that can reduce measurement data while increasing the restoration rate of the original signal.

Means for Solving the Problems

[0008] The above problems of the present invention are solved by the following means. A measuring device comprising a preprocessing unit that preprocesses a time-varying signal to be measured, and a measurement unit that randomly measures the preprocessed signal based on a predetermined first random matrix Φ, wherein the preprocessing unit downsamples a signal obtained by shifting the signal to be measured downward in frequency by a specific frequency.

Effects of the Invention

[0009] According to the present invention, it is possible to reduce measurement data while increasing the restoration rate of the original signal.

Brief Description of the Drawings

[0010]

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Embodiments for Carrying Out the Invention

[0011] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Note that each drawing only schematically shows the present invention to such an extent that it can be sufficiently understood. Therefore, the present invention is not limited only to the illustrated examples. Also, in each drawing, common components and similar components are denoted by the same reference numerals, and redundant descriptions thereof are omitted.

[0012] (First Embodiment) FIG. 1 is a configuration diagram of the measurement system according to the embodiment of the present invention. The measurement system 100 measures the characteristics (for example, vibration velocity) of the measurement object 30 with the sensor 20, and the random measurement device 10 and the measurement arithmetic device 50 are communicably connected. The measurement object 30 is, for example, an ultrasonic horn. The sensor 20 is, for example, a Doppler vibrometer, detects the vibration velocity of the measurement object 30, and outputs a measured signal a(t) that changes over time.

[0013] The random measurement device 10 preprocesses the measured signal a(t) output by the sensor 20 and randomly samples the preprocessed signal s(t). The random measurement device 10 includes a preprocessing unit 40, a random measurement unit 1 as a measurement unit, a random matrix setting unit 2 as a setting unit, and a receiving unit 4. In other words, the measurement method executed by the random measurement device 10 includes a preprocessing process and a random measurement process.

[0014] Figure 2 is a configuration diagram showing an evaluation target facility for evaluating a measurement target. The evaluation target facility 150 includes a measurement target 30 and a sensor 20. The measurement target 30 is, for example, an ultrasonic horn and includes a vibrator 35 and a horn 36. The vibrator 35 includes a piezoelectric element 31 and a bolt 32. Since the piezoelectric element 31 is brittle with respect to tension, it is tightened with the bolt 32 and used in a state where a compressive load is applied. The horn 36 amplifies vibrations. Note that the ultrasonic horn, which is the measurement target 30, is measured while being leaned vertically. The sensor 20 is, for example, a laser Doppler vibrometer that detects the vibration speed of the measurement target 30. The sensor 20 measures the vibration speed by applying laser light to the upper surface of the vibrator 35 of the leaned measurement target 30.

[0015] Figure 3 is a configuration diagram of the preprocessing unit 40 used in the measurement system according to the first embodiment of the present invention. The preprocessing unit 40 preprocesses the measured signal a(t) output by the sensor 20 and outputs a preprocessed signal s(t). The preprocessing unit 40 converts the frequency so as to display a specific frequency range f1 to f2 in the range of 0 to f (frequency range Hz). By this conversion, the width of Δ = f2 - f1 is enlarged and displayed M times (Δ·M = f) to the width of f. This function is called a zoom function. The preprocessing unit 40 includes a sampling unit 41, a band-pass filter 45, a frequency shift 42, a low-pass filter 43, and a downsampling unit 44.

[0016] The sampling unit 41 digitally converts the signal to be measured a(t) at the first sampling frequency (for example, 256 kHz) and outputs a sampling signal SP(t). The band-pass filter 45 passes the frequency range f1~f2 to be Zoomed and outputs a band-pass signal BPF(t). The frequency shift 42 performs a frequency shift of a specific frequency (fm = 30 kHz) on the band-pass signal BPF(t). That is, the frequency shift 42 is a multiplier that multiplies the sampling signal SP(t) with a sine wave signal M(t) of a specific frequency (fm = 30 kHz). This multiplier outputs signals (output signals) of both the signal component FSh(t) of the upper side frequency (Fs1 / 2 + fm = 128 kHz + 30 kHz) and the signal component FSl(t) of the lower side frequency (Fs1 / 2 - fm = 128 kHz - 30 kHz).

[0017] That is, the signal component FSh(t) is obtained by shifting the frequency of the sampling signal SP(t) upward by a specific frequency (fm = 30 kHz). Also, the signal component FSl(t) is obtained by shifting the frequency of the sampling signal SP(t) downward by a specific frequency (fm).

[0018] The low-pass filter 43 blocks the upper side frequency component FSh(t) of the upper side frequency (fs1 + fm) and outputs the lower side frequency component FSl(t) of the lower side frequency (fs1 - fm). That is, the low-pass filter 43 outputs a signal obtained by shifting the frequency of the sampling signal SP(t) downward by a specific frequency (fm). As a result, the sampling frequency can be lowered, and the number of samples is reduced (Zoom function). The downsampling unit 44 downsamples the lower side frequency component FSl(t) at a second sampling frequency (for example, fs2 = 640 Hz) lower than the first sampling frequency (for example, fs1 = 256 kHz) and outputs a preprocessed signal s(t).

[0019] Figure 4 is a diagram showing an example of waveforms of each part in the preprocessing unit. (a) is the sampling signal SP(t) obtained by sampling the signal to be measured a(t) by the sampling unit 41 at the first sampling frequency. (b) is the frequency-shifted signal FS(t) shifted by 30 kHz. (c) is the lower frequency component FSl(t) that has passed through the low-pass filter 43. (d) is the preprocessing signal s(t) obtained by downsampling the lower frequency component FSl(t).

[0020] Returning to the description of FIG. 1, the random measurement unit 1 outputs (transmits) to the measurement arithmetic device 50 a signal of a random measurement vector y = Φs, which is a vector representation of random measurement values obtained by randomly sampling the preprocessing signal s(t) according to the first random matrix Φ. Here, the measurement period is divided into a parameter setting period (first period) for setting measurement parameters (for example, the regularization coefficient λ described later) and a measurement period (second period) after the parameter setting.

[0021] FIG. 5 is a diagram for explaining the relationship between the parameter setting period (first period T1) and the measurement period (second period T2) after the parameter setting. The first period T1 is from t = 0 to t1, and the second period T2 is after t = t2. Note that the period from t1 to t2 is a measurement interruption period.

[0022] Let the random measurement vector measured in the first period T1 be the first random measurement vector y1 = Φs, and the random measurement vector (second random measurement vector) measured in the second period T2 be y = Φs. Here, the first random matrix Φ includes a matrix Φr indicating that the columns of all time-series signals of the preprocessing signal s(t) (discrete-time signal s) are randomly decimated, and a matrix Φrsu indicating that measurements are performed a plurality of times to randomly set the measurement start timing of the discrete-time signal s. The matrix Φ r indicates that measurements are performed so as to randomly decimate the columns of all time-series signals (discrete-time signal s) obtained by equally spacing the preprocessing signal s(t).

[0023] The matrix Φrsu performs, in one measurement, a constant frequency f rsu (f rsu << sampling frequency fs) or a constant frequency frsu of M p It is assumed that data at points is taken. As a result, the number of samples by which the random measurement unit 1 samples the preprocessing signal s(t) decreases compared to the number of discrete-time signals s. Since the random measurement unit 1 performs compressed sampling (CS: Compressed Sensing) on the preprocessing signal s(t), it can be manufactured at a lower cost than outputting a column of all time-series signals (discrete-time signal s).

[0024] The random matrix setting unit 2 sets the first random matrix Φ used by the random measurement unit 1. The first random matrix Φ may be fixed, but in this embodiment, with the second random matrix Φ0 as an initial value, the first random matrix Φ is obtained by updating the second random matrix Φ0. The receiving unit 4 receives the update data (first random matrix Φ) of the random matrix setting unit 2 from the measurement arithmetic device 50.

[0025] In the second period T2 (FIG. 5), the measurement arithmetic device 50 restores the discrete-time signal s from the random measurement values (random measurement vector y = Φs) received from the random measurement device 10. That is, the measurement arithmetic device 50 restores all data (discrete-time signal s) from a small amount of data (y = Φs) received from the random measurement device 10. Here, when the discrete-time signal s is expressed as the coefficient x of the n×n orthogonal basis matrix ψ with the basis vectors {Ψ i} as columns, s = ψx. Here, the basis vectors {Ψ i} are, for example, Fourier basis vectors with time t as a variable. Note that the time resolution of the Fourier basis vectors is, for example, (downsampling frequency / downsampling number) / compression ratio of compressed sampling.

[0026] The measurement and calculation device 50 is a PC (Personal Computer) configured to include a receiving unit 55, a control unit 60, and a transmitting unit 56. The receiving unit 55 receives data of a random measurement vector y = Φs from the random measurement device 10. The control unit 60 is a computer having a CPU (Central Processing Unit), and realizes the functions of an estimation unit 61, a regularization coefficient setting unit 62, and a restoration unit 63 by executing a measurement and calculation program.

[0027] The estimation unit 61 estimates the coefficient x of the n×n orthogonal basis matrix ψ using the random measurement vector y = Φs received by the measurement and calculation device 50. Specifically, when using the LASSO (Least Absolute Shrinkage and Selection Operator) method and setting the regularization coefficient as λ0, the coefficient x = {x i} is estimated so that the following equation (1) is minimized.

Equation

[0028] Here, the norms in the mathematical expressions are defined by the following equations (2) and (3).

Equation

Equation

[0029] Σ|x i | means adding the absolute values of x i from i = 1 to N, and Σ|x i | 2 means adding the squares of the absolute values of x i from i = 1 to N. Note that (y - Φψx), which is obtained by subtracting the product Φψx of the first random matrix Φ, the n×n orthogonal basis matrix ψ, and its coefficient x from the random measurement vector y, represents the error.

[0030] Before estimating the coefficient x of the n×n orthogonal basis matrix ψ in the second period T2 (FIG. 5), the regularization coefficient setting unit 62 sets in advance the value of the regularization coefficient λ0 in the first period T1 to be the maximum within the standard deviation of cross-validation for the regularization coefficient λ with the least error. At this time, for the first random matrix Φ, the initial value (second random matrix Φ0) stored in the random matrix setting unit 2 of the random measurement device 10 is used, but it may be changed as appropriate.

[0031] In the second period T2, the restoration unit 63 multiplies the n×n orthogonal basis matrix ψ by the coefficient x = {x i} estimated by the estimation unit 61 to restore the discrete-time signal s = ψx. That is, the restoration unit 63 can restore the entire discrete-time signal s using the randomly sampled random measurement vector y = Φs.

[0032] When the regularization coefficient setting unit 62 determines the value of the regularization coefficient λ0, if the first random matrix Φ is changed without using the second random matrix Φ0, the transmission unit 56 transmits the changed first random matrix Φ to the random measurement device 10. As a result, the value of the random matrix setting unit 2 of the random measurement device 10 is updated from the second random matrix Φ0 to the first random matrix Φ.

[0033] FIG. 6 is a flowchart for explaining the operation of the measurement system according to the first embodiment of the present invention. This flow starts first when the measurement target 30 (FIGS. 1 and 2) is changed. Thereby, the measurement arithmetic unit 50 predetermines parameters (regularization coefficient λ and first random matrix Φ) in the first period T1 (FIG. 5) and starts measurement in the second period T2 (FIG. 5). Also, the random matrix Φ = Φ0 is set (stored) in advance in the random matrix setting unit 2.

[0034] In the first period T1, the preprocessing unit 40 (Figs. 1 and 3) of the random measurement device 10 performs preprocessing on the measured signal a(t) from the sensor 20 and outputs a preprocessed signal s(t). Then, the random measurement unit 1 (Fig. 1) of the random measurement device 10 pre-acquires the preprocessed signal s(t) (step S1). That is, the random measurement device 10 acquires a discrete-time signal s downsampled at a second sampling frequency (e.g., fs2 = 640 Hz). The random measurement device 10 calculates a random measurement vector y = Φs using the pre-acquired discrete-time signal s (step S2). After the process of step S2, the random measurement device 10 transmits the random measurement vector y to the measurement calculation device 50 (step S3). The measurement calculation device 50 receives the random measurement vector y (step S4) and determines a regularization coefficient λ = λ0 such that it becomes the maximum value within the standard deviation of cross-validation at λ with the least error (step S5). At this time, the regularization coefficient setting unit 62 (Fig. 1) uses the random matrix Φ = Φ0, but the first random matrix Φ may be appropriately modified and then the regularization coefficient λ0 may be determined.

[0035] After the process of step S5, the measurement calculation device 50 transmits the appropriately modified first random matrix Φ to the random measurement device 10 (step S6). Thereby, the first random matrix Φ is set in the random measurement device 10. The random measurement device 10 receives the first random matrix Φ and re-sets the second random matrix Φ0 set in the random matrix setting unit 2 to the received first random matrix Φ (step S7). Thereby, the random measurement device 10 completes the preparation for starting the measurement.

[0036] In the second period T2 (FIG. 5), the random measurement device 10 randomly acquires the preprocessing signal s(t) from the sensor 20 (step S8). At this time, the first random matrix Φ reset in step S7 is stored in the random matrix setting unit 2. During the execution of step S8, the random measurement device 10 calculates the random measurement vector y = Φs using the randomly acquired preprocessing signal s(t) (step S9). After the process of step S9, the random measurement device 10 transmits the random measurement vector y to the measurement calculation device 50 (step S10). The measurement calculation device 50 receives the random measurement vector y (step S11) and determines the coefficients x = {x i} of the n×n orthogonal basis matrix ψ using the LASSO method (step S12). After the process of step S12, the measurement calculation device 50 restores the discrete-time signal s = ψx.

[0037] As described above, according to the measurement system 100 of the present embodiment, the preprocessing unit 40 shifts the input signal a(t) to a lower frequency (fs1 - fm) lower than the first sampling frequency fs1. Therefore, the preprocessing unit 40 can perform downsampling at the second sampling frequency fs2. As a result, since the preprocessing unit 40 performs downsampling and the random measurement unit 1 performs random sampling, the number of samplings is reduced in an overlapping manner. In other words, the number of data of the random measurement vector y transmitted from the random measurement device 10 to the measurement calculation device 50 becomes extremely small. Conversely, if the number of samplings is the same, the frequency resolution of the coefficients x = {x i} estimated by the estimation unit 61 is increased.

[0038] (Second Embodiment) In the first embodiment, it was determined so as to be "the maximum value within the standard deviation of cross-validation at λ where the regularization coefficient λ = λ0 has the least error" (step S5 in FIG. 6). In this embodiment, the error is calculated by the difference between the sum of products of powers calculated by compressive sampling (CS: Compressed Sensing) and the sum of products of powers calculated by DFT (Discrete Fourier Transform) operation.

[0039] FIG. 7 is a configuration diagram of a measurement system according to a second embodiment of the present invention. The measurement system 101 is configured by communicably connecting a random measurement device 11, a sequential measurement device 71, and a measurement arithmetic unit 51.

[0040] The random measurement device 11 includes the above-described preprocessing unit 40 and a random measurement unit 1 as a random measurement value output unit. In particular, for the matrix Φ indicating a random start rsu at this time, the sampling frequency fs = Nf rsu is obtained.

[0041] The sequential measurement device 71 includes the above-described preprocessing unit 40, a sequential measurement unit 73, a DFT arithmetic unit 74, and a sampling frequency generator 76. The sampling frequency generator 76 generates a clock of the second sampling frequency fs2 described above. The sequential measurement unit 73 sequentially measures the preprocessing signal s(t) using the second sampling frequency fs2. The sequential measurement unit 73 is different from the random measurement unit 1 in that it does not measure randomly.

[0042] The DFT (Discrete Fourier Transform) arithmetic unit 74 performs a discrete Fourier transform on the discrete time signal s output by the sequential measurement unit 73 and outputs the calculation result (Fourier coefficient xf = {xf i}) to the measurement arithmetic unit 52. Note that the calculation for the preprocessing signal s(t) is called ZoomDFT.

[0043] The measurement arithmetic unit 51 checks the Fourier coefficient xf = {xf i} in the first period T1 (FIG. 5), makes a sparsity determination, and sets a parameter (regularization coefficient λ). Specifically, in the first period T1, the measurement arithmetic unit 51 checks that n > m and n / s > n / m when the constant of compressive sensing is c. Here, let m be the number of samples after compression, n be the number of samples before compression, and s be the number of components of q (frequency) that is not zero. Then, the measurement arithmetic unit 51 sets a parameter (regularization coefficient λ).

[0044] Also, in the second period T2 (FIG. 5), the measurement operation device 51 restores all data (discrete-time signal s) from a small amount of random measurement values (random measurement vector y = Φs) received from the random measurement device 11, similar to the measurement operation device 50 (FIG. 1).

[0045] The measurement operation device 51 is a PC, and by executing a measurement operation program, it realizes the functions of an estimation unit 61, a regularization coefficient setting unit 62, a restoration unit 63, a restoration error calculation unit 54, an abnormality degree calculation unit 57, and a notification unit 58.

[0046] In the first period T1, the restoration error calculation unit 54 calculates the sum of the squares of the differences between the Fourier coefficients xf = {xf i} and the coefficients x = {x i}, and obtains the power difference between the discrete-time signal s and the first random measurement value (the vector representation is the first random measurement vector y1). Further, the restoration error calculation unit 54 divides the power difference by the sum of the squares of the coefficients x to calculate the restoration error r (Equation (4)). The restoration error calculation unit 54 confirms that the restoration error r falls within a predetermined range (for example, 0.01%, 0.1%, 1%, 10%, 20%). If it does not fall within the predetermined range, the regularization coefficient λ = λ0 is corrected.

[0047]

Equation

[0048] In the second period, the abnormality degree calculation unit 57 calculates the abnormality degree using, for example, the Mahalanobis distance (online). When the abnormality degree calculation unit 57 detects an abnormality, that is, when the abnormality degree using the Mahalanobis distance exceeds the threshold value, the notification unit 58 notifies the user.

[0049] FIG. 8 is a flowchart for explaining the operation of the measurement system according to the second embodiment of the present invention. In the first period T1 (FIG. 5), in the sequential measurement device 71, the sequential measurement unit 73 sequentially acquires the preprocessing signal s(t) at a predetermined second sampling frequency fs2 (step S21). After the processing of step S21, in the sequential measurement device 71, the DFT calculation unit 74 calculates the Fourier coefficients xf = {xf i} (step S22), and transmits the Fourier coefficients xf to the measurement calculation device 51 (step S23).

[0050] In the measurement calculation device 51, the regularization coefficient setting unit 62 determines the regularization coefficient λ0 using the first random measurement vector y1 = Φs (step S24). In the measurement calculation device 51, the Fourier coefficients xf are received (step S25), and the restoration error calculation unit 54 calculates the restoration error r and determines whether the restoration error r is within a predetermined range (step S26). When the restoration error r is outside the predetermined range (outside the predetermined range in step S26), the measurement calculation device 51 returns the process to step S24 and causes the regularization coefficient setting unit 62 to reset the regularization coefficient λ0. On the other hand, when the restoration error r is within the predetermined range (within the predetermined range in step S26), the measurement system 101 shifts to the second period T2 (FIG. 5).

[0051] In the second period T2, in the random measurement device 11, the random measurement unit 1 randomly acquires the measurement value of the preprocessing signal s(t) (step S27), and transmits the random measurement vector y = Φs to the measurement calculation device 51 (step S28). In the measurement calculation device 51, the random measurement vector y = Φs is received (step S29), and the estimation unit 61 estimates the coefficients x = {x i} (step S30). The estimation for the preprocessing signal s(t) is called ZoomCS.

[0052] After the process of step S30, in the measurement and calculation device 51, the abnormality degree calculation unit 57 calculates the abnormality degree and determines whether the abnormality degree exceeds the threshold value α (step S31). If the abnormality degree is equal to or less than the threshold value α (below the threshold value in step S31), the measurement and calculation device 51 returns the process to step S29 and continues to receive the random measurement vector y = Φs. On the other hand, if the abnormality degree exceeds the threshold value α (exceeds the threshold value in step S31), the measurement and calculation device 51 causes the notification unit 58 to perform notification (step S32).

[0053] FIG. 9 is a diagram showing a frequency spectrum measured by the measurement system 101 according to the second embodiment of the present invention. The horizontal axis represents frequency [Hz], and the vertical axis represents the speed [m / s] at which the measurement target 30 vibrates. The thick solid line is the result of ZoomCS. The thin solid line is the result of ZoomDFT, and the broken line is the result of ZoomFFT. The white circles (○) are the results of ZoomDFT with correction processing, and the black circles (●) are the results of ZoomCS with correction processing. That is, the speed [m / s] on the vertical axis is such that the thick solid line corresponds to the coefficient x = {x i}, and the thin solid line and the broken line correspond to the Fourier coefficients xf = {xf i}

[0054] ZoomFFT downsamples the measured signal a(t) with the first sampling frequency fs1 = 256 kHz at the second sampling frequency fs2 = 640 Hz and performs an FFT operation on 512 points of data. That is, the frequency resolution is 640 Hz / 512 = 1.25 Hz. ZoomDFT performs a DFT operation on 25,600 points of data downsampled at the second sampling frequency fs2 = 640 Hz for 40 seconds. That is, the frequency resolution is 640 Hz / 25,600 = 0.025 Hz.

[0055] ZoomCS randomly sampled 25,600 data points every 12.8 Hz (640 / 50) for 40 seconds. That is, ZoomCS further compressed and sampled 512 data points downsampled at 640 Hz by a factor of 1 / 50. That is, the frequency resolution is (640 Hz / 512) / 50 = 0.025 Hz. As a result, ZoomCS estimates 25,600 data points (40 s) at 640 Hz with 512 data points, which is 1 / 50 of the 25,600 data points.

[0056] Both ZoomCS (thick solid line) and ZoomDFT (thin solid line) have a frequency resolution of 0.025 Hz, and the frequency spectra of the vibration velocity match very well. Therefore, the restoration error calculation unit 54 can confirm that the restoration error r is within a predetermined range. That is, the restoration error calculation unit 54 calculates the sum of the squares of the differences between the Fourier coefficients xf = {xfi} by ZoomDFT and the coefficients x = {xi} by ZoomCS, and can confirm that the restoration error r (Equation (7)), which is the result of the calculation (power difference) divided by the sum of the squares of the coefficients x, is within a predetermined range.

[0057] By the way, the frequency spectrum of ZoomFFT (dashed line) does not match that of ZoomCS and ZoomDFT. This is because the frequency resolution of ZoomFFT is 1.25 Hz, which is significantly different from ZoomCS and ZoomDFT. Therefore, correction is performed to change the frequency resolution for the frequency spectra of ZoomDFT and ZoomCS.

[0058] ZoomDFT (○) and ZoomCS (●) are subjected to bundling processing on the frequency axis. The bundling processing is resampling processing in the frequency domain using DFT and is a method of bundling by a compression ratio. According to this bundling processing, ZoomDFT (○) and ZoomCS (●) after correction processing almost match ZoomFFT (dashed line). That is, if the frequency resolution is made the same, the frequency spectrum of ZoomFFT almost matches the frequency spectra of ZoomCS and ZoomDFT.

[0059] As described above, according to the present embodiment, the restoration error calculation unit 54 (FIG. 7) can confirm that the restoration error r is within a predetermined range (S26 (FIG. 8)). Thereby, it is determined that the determined regularization coefficient λ = λ0 (S24 (FIG. 8)) is appropriate.

[0060] (Third Embodiment) In the measurement system of each of the above embodiments, in the second period T2, using the random measurement vectors y = Φs sequentially received by the measurement calculation devices 50 and 51, the coefficients x = {x i} were sequentially estimated. However, the random measurement vectors y = Φs sequentially received by the measurement calculation device can be stored in the storage unit, and batch processing can be performed using the random measurement vectors y = Φs stored in the storage unit.

[0061] FIG. 10 is a configuration diagram of a measurement system according to the third embodiment of the present invention. The measurement system 103 includes a random measurement device 11, a measurement calculation device 52, and a sequential measurement device 71. The random measurement device 11 and the sequential measurement device 71 have the same configuration as in the second embodiment. The measurement calculation device 52 is different from the measurement calculation device 51 (FIG. 7) of the second embodiment in that it includes a storage unit 59.

[0062] The storage unit 59 stores the random measurement vectors y = Φs in the second period T2 (FIG. 5). Thereby, the measurement calculation device 52 determines the regularization coefficient λ = λ0 using the first random measurement vector y1 = Φs received in the first period T1, and in the second period T2, the random measurement vectors y = Φs are stored in the storage unit 59. Thereafter, in batch processing, the restoration unit 63 restores the discrete-time signal s = ψx.

[0063] (Fourth Embodiment) In the second embodiment, in the first period T1 (FIG. 5), the random measurement device 10 (FIG. 1) randomly acquired the preprocessing signal s(t). However, the preprocessing signal s(t) may be sequentially measured at a predetermined second sampling frequency fs2, and randomly selected from the sequentially measured data.

[0064] FIG. 11 is a configuration diagram of a measurement system according to a fourth embodiment of the present invention. The measurement system 104 includes a random measurement device 11, a sequential measurement device 71, and a measurement arithmetic unit 53. The random measurement device 11 and the sequential measurement device 71 have the same configuration as in the second embodiment.

[0065] The measurement arithmetic unit 53 includes a restoration error arithmetic unit 54, an abnormality degree arithmetic unit 57, a notification unit 58, an estimation unit 61, a regularization coefficient setting unit 62, and a restoration unit 63, similar to the measurement arithmetic unit 52 of the second embodiment. However, the measurement arithmetic unit 51 is different from the measurement arithmetic unit 52 of the above embodiment in that it includes a random selection unit 67 and a switch 68.

[0066] The random selection unit 67 randomly selects the discrete-time signal s sequentially output by the sequential measurement unit 73 according to the first random matrix Φ in the first period T1. That is, the random selection unit 67 also functions as a random measurement value output unit, and outputs a first random measurement vector y1 = Φs obtained by expressing the random measurement value in vector form. The switch 68 is a single-circuit two-contact switch that sets the terminal j to either the terminal h or the terminal i. The i terminal is connected to the output of the random selection unit 67, the h terminal is connected to the output of the random measurement unit 1, and the j terminal is connected to the input of the estimation unit 61. In the estimation unit 61, the variable of the Fourier basis vector {Ψ i} is the time t.

[0067] In the first period T1, similar to the first embodiment, the estimation unit 61 inputs the first random measurement vector y1 = Φs output by the random selection unit 67, and estimates the coefficient x of the n×n orthogonal basis matrix ψ. At this time, the value of the regularization coefficient λ0 is set to be the maximum value within the standard deviation of cross-validation at λ with the least error. Further, when the restoration error r is not within a predetermined range, the restoration error calculation unit 54 resets the regularization coefficient λ0. Note that although the random measurement unit 1 also outputs the first random measurement vector y1 = Φs, it is blocked by the switch 68.

[0068] In the second period T2, the estimation unit 61 inputs the random measurement vector y = Φs output by the random measurement unit 1, using the regularization coefficient λ0 set in the first period T1, and estimates the coefficient x of the n×n orthogonal basis matrix ψ. Further, similar to the second and third embodiments, the restoration unit 63 restores the discrete-time signal s.

[0069] (Fifth Embodiment) The measurement system of each of the above embodiments measures the vibration of an ultrasonic horn or the like, but a rotating device 33 (FIG. 12) such as a bearing may be used as a measurement target. At this time, vibration analysis using the rotation speed can be performed.

[0070] FIG. 12 is a configuration diagram of the measurement system according to the fifth embodiment of the present invention. The measurement system 105 measures the characteristics (for example, vibration) of the rotating device 33 with the sensor 21, and the random measurement device 12 and the measurement arithmetic unit 50 are communicably connected. The rotating device 33 is, for example, a bearing and includes a rotating electric machine such as a motor or a generator. The sensor 20 is, for example, an acceleration sensor and detects the vibration of the rotating device 33. Further, the rotation angle sensor 39 outputs a rotation phase θ indicating the rotation position of the rotating device 33.

[0071] The random measurement device 12 preprocesses the measured signal a(t) output by the sensor 21, and randomly samples the preprocessed signal s(t) in synchronization with the rotation phase θ. The random measurement device 12 includes a preprocessing unit 40, a random matrix setting unit 2 as a setting unit, and a receiving unit 4, similar to the random measurement device 10 (FIG. 1) of the first embodiment. However, the random measurement device 12 is different from the random measurement device 10 in that it has a random measurement unit 5 instead of the random measurement unit 1 and further includes a rotation information acquisition unit 3. The rotation information acquisition unit 3 detects the rotation position of the rotating device 33 and outputs it to the random measurement unit 5 as a signal of the rotation phase θ. The random measurement unit 5 synchronizes the preprocessing signal s(t) with the rotation phase θ and outputs (transmits) a signal of a random measurement vector y = Φs, which is a vector representation of random measurement values randomly sampled according to the first random matrix Φ, to the measurement arithmetic device 50.

[0072] FIG. 13 is a configuration diagram showing a measurement target facility for inspecting a measurement target. The measurement target facility 151 includes a rotating device 33 of the measurement target, a motor 38, a sensor 21, and a rotation angle sensor 39. The rotating device 33 is, for example, a bearing having an inner ring 33a and an outer ring 33b. The rotating device 33 has a damaged outer ring 31b as an evaluation target. The inner ring 33a of the rotating device 33 is rotated by the motor 38. The rotation angle sensor 39 detects the rotation position of the inner ring 33a and outputs the rotation phase θ. The sensor 21 is an acceleration sensor that detects the vibration of the rotating device 33. The random measurement unit 1 synchronizes the preprocessing signal s(t) with the rotation phase θ and outputs (transmits) a signal of a random measurement vector y = Φs, which is a vector representation of random measurement values randomly sampled according to the first random matrix Φ, to the measurement arithmetic device 50.

[0073] FIG. 14 is a diagram for explaining the difference in the number of samples of the preprocessing signal s(t) depending on the high or low rotation speed. The horizontal axis represents time t, and the vertical axis in the following figure represents the preprocessed signal s(t). The preprocessed signal s(t) is a sine wave signal. Assume that the first cycle from time 0 to t1 has a high rotational speed, and the second cycle from time t1 to t2 has a low rotational speed. In the following figure, the points where the preprocessed signal s(t) is sampled in synchronization with the rotational phase are indicated by white circles (○). For example, in the lower figure of FIG. 14, white circles (○) are marked every 40° of the rotational phase. Also, vertical lines at the same timing are marked on the horizontal line in the upper figure. The number of samples per cycle is the same in both the high rotational speed region A and the low rotational speed region B.

[0074] Note that a phenomenon that occurs once per rotation (one cycle) is defined as a rotational first-order component, and its n times is defined as a rotational nth-order component. The analysis performed by taking the X-axis as the order and the Y-axis as the magnitude of the vibration noise of the order component is called "rotational order ratio analysis".

[0075] FIG. 15A is a diagram showing the time change of the measurement signal. The horizontal axis is time t, and the vertical axis is the preprocessed signal s(t). Also, FIG. 15B is a diagram showing the time change of the rotational phase of the rotating device. The horizontal axis is time t, and the vertical axis is the rotational phase θ(t). Here, assume that the preprocessed signal s(t) is a sine wave signal whose frequency gradually increases. Black circles (●) are attached to a plurality of measurement points a, b, c, d of the preprocessed signal s(t) and the rotational phase θ(t).

[0076] In FIG. 15B, at time t = 0, the rotational phase θ(0) = 0, and the rotational phase θ(t) monotonically increases with the passage of time (measurement points a → b → c → d). For example, at point b (FIG. 15A), since it is before the third cycle, the rotational phase is less than (360×4)°. At point c (FIG. 15A), since it is before the fifth cycle, the rotational phase is more than (360×4)°. At point d (FIG. 15A), it is after the sixth cycle, and the rotational phase is between (360×4)° and (360×8)°.

[0077] FIG. 15C is a diagram showing the relationship between the measurement signal and the rotational phase. The horizontal axis is the rotational phase θ, and the vertical axis is the preprocessed signal s(θ). Between c and d, although the time T3 (FIG. 15A) is short, the rotational phase width Θ1 is expressed as long. In other words, as shown in FIG. 15C, if the rotational phase θ is used as a variable, even if the rotational speed of the rotating device 33 changes, the preprocessing signal s(θ) can be evaluated as a sine wave.

[0078] As described above, according to the measurement system 105 (FIG. 12) of the present embodiment, the random measurement unit 1 measures in synchronization with the rotational phase θ of the rotating device 33. As a result, the estimation unit 61 of the measurement arithmetic device 50 (FIG. 12) estimates the coefficient x = {x i} not for each frequency but for each order ratio x = {x i}. Further, the basis vectors {Ψ i} are, for example, Fourier basis vectors with the rotational phase θ as a variable, and one cycle of the Fourier basis vectors corresponds to one rotation of the rotating device 33.

[0079] As described above, according to the measurement system 105 of the present embodiment, order ratio analysis with a reduced number of measurement points can be performed. That is, in the measurement system 105, frequency components (specific frequency components) at an order ratio (specific order ratio) specified based on the rotational angular velocity (ω = dθ / dt) measured in the first period T1 can be Zoomed and measured.

[0080] (Sixth Embodiment) FIG. 16 is a configuration diagram of a measurement system according to the sixth embodiment of the present invention. The measurement system 106 is configured to include a random measurement device 10 and a measurement arithmetic device 77, similar to the measurement system 100 (FIG. 1) of the above embodiment. However, the random measurement device 13 is connected to a general-purpose sensor 22 instead of the sensor 20 (FIG. 1). That is, the general-purpose sensor 22 is connected to the preprocessing unit 40 included in the random measurement device 13. The general-purpose sensor 22 is, for example, a general-purpose microphone made of MEMS, and has poor frequency characteristics compared to when the measurement sensor is used as the sensor 21 (FIG. 12).

[0081] FIG. 17 is a diagram showing the frequency characteristics of a measurement microphone, a high-frequency measurement microphone, and a general-purpose microphone made of MEMS. The horizontal axis is the frequency [Hz]. The vertical axis is in decibels, with 0 decibels at the reference frequency of 1 kHz. The measurement microphone maintains flat frequency characteristics from about 10 Hz to about 20 kHz. In contrast, a general-purpose microphone made of MEMS has a reduced output at low frequencies from 20 Hz to about 200 Hz. Also, a microphone for high-frequency measurement can be used up to about 10 Hz to 100 kHz.

[0082] The measurement arithmetic unit 77 (FIG. 16) differs from the measurement arithmetic unit 50 (FIG. 1) in that it includes a frequency correction unit 69. The frequency correction unit 69 corrects the frequency characteristics of the random measurement vector y received by the receiving unit 55. Specifically, the frequency correction unit 69 increases the gain at low frequencies from about 20 Hz to about 200 Hz to make the frequency characteristics including the general-purpose sensor 22 comparable to those of the measurement sensor.

[0083] (Seventh Embodiment) FIG. 18 is a configuration diagram of a measurement system according to the seventh embodiment of the present invention. Similar to the measurement system 103 (FIG. 10) of the fourth embodiment, the measurement system 104 includes a random measurement device 13, a measurement arithmetic unit 78, and a sequential measurement device 71. The random measurement device 13 further includes a switch 7, and is different from the random measurement device 11 (FIG. 10) in that the switch 7 switches to either the general-purpose sensor 22 or the measurement sensor 23 and connects to the preprocessing unit 40.

[0084] The measurement and calculation device 78 differs from the measurement and calculation device 52 (Fig. 10) in that it further includes a frequency correction unit 69 and a switch 68. Also, the sequential measurement device 72 connects a measurement sensor 23 instead of the sensor 21 (Fig. 12). This measurement sensor 23 may be a measurement microphone (Fig. 17). Furthermore, the measurement sensor 23 may be a high-frequency measurement microphone (Fig. 17) capable of measuring up to a high frequency (~100 kHz). Also, the measurement sensor 23 may be a Doppler vibrometer. The frequency correction unit 69 is connected to the storage unit 59 and corrects the frequency characteristics of the data of the general-purpose sensor 22 (random measurement vector y = Φs) stored in the storage unit 59. Thereby, the general-purpose sensor 22 and the frequency correction unit 69 as a whole become equivalent to the measurement sensor 23.

[0085] The switches 7, 68 are two-contact switches that connect either one of the terminals a, b to the terminal c. The switches 7, 68 are connected to the terminal b in the first period T1 (Fig. 5) and are connected to the terminal a in the second period T2 (Fig. 5). That is, the switch 2 connects the measurement sensor 23 and the preprocessing unit 40 in the first period T1 and connects the general-purpose sensor 21 and the preprocessing unit 40 in the second period T2. The switch 68 connects the storage unit 59, the estimation unit 61, and the regularization coefficient setting unit 62 in the first period T1 and connects the frequency correction unit 69, the estimation unit 61, and the regularization coefficient setting unit 62 in the second period T2.

[0086] (Comparative Example) In each of the above embodiments, the preprocessing signal s(t) was restored by compressive sampling (CS), but the preprocessing signal s(t) may be restored by DFT conversion without performing compressive sampling.

[0087] Fig. 19 is a configuration diagram of a measurement system that is a comparative example of the present invention. The measurement system 106 is configured such that the measuring device 14 and the measurement computing device 70 are communicably connected. The measuring device 14 includes the above-described preprocessing unit 40 and the sequential measurement unit 6. The preprocessing unit 40 preprocesses the measured signal a(t) of the sensor 20 and outputs a preprocessed signal s(t). The sequential measurement unit 6 sequentially acquires the preprocessed signal s(t) at the second sampling frequency fs2 and outputs a discrete-time signal s. That is, the measuring device 14 is different from the random measuring devices 10 (FIG. 1), 11 (FIGS. 7, 10, 11), and 12 (FIG. 12) of the above embodiments in that it does not sample randomly.

[0088] The measurement computing device 79 includes a receiving unit 55, an x computing unit 64, and a restoration unit 65. The receiving unit 55 receives the discrete-time signal s from the measuring device 14. The x computing unit 64 computes the coefficient (Fourier coefficient xf) of the Fourier basis vector ψf. Here, the variable of the Fourier basis vector ψf is time. That is, the x computing unit 64 performs a discrete Fourier transform on the discrete-time signal s in the same manner as the DFT computing unit 74 (FIGS. 7, 10, 11). The restoration unit 65 restores the discrete-time signal s = ψf·xf using the Fourier basis vector ψf and the Fourier coefficient xf.

[0089] Also, since the sequential measurement unit 6 sequentially acquires the preprocessed signal s(t) at the second sampling frequency fs2, the measurement computing device 53 can perform a fast Fourier transform. However, in the above embodiments, since the preprocessed signal s(t) is randomly sampled, a discrete Fourier transform cannot be performed. However, in the measurement computing devices 50 (FIG. 1), 51 (FIG. 7), 52 (FIG. 10), and 53 (FIG. 11) of the above embodiments, the coefficient x of the n×n orthogonal basis matrix ψ is made sparse by solving L1 regularization by LASSO (Least Absolute Shrinkage and Selection Operator).

[0090] (Modification example) The present invention is not limited to the above embodiments, and can be modified without departing from the spirit of the present invention. For example, there are the following. (1) In the preprocessing unit 40 (Fig. 3) of the above-described embodiment, although the zoom function was performed, envelope processing can be added. The preprocessing unit 49 shown in Fig. 20 includes a sampling unit 41, a BPF 45a, an absolute value detection unit 47, a BPF 45b, a frequency shift 42, a low-pass filter 43, a downsampling unit 44, and a BPF processing unit 46. Thereby, the preprocessing unit 49 converts the frequency so as to display a specific frequency range f1 to f2 in the range of 0 to f (frequency range Hz).

[0091] The sampling unit 41 samples the signal a(t) to be measured at the first sampling frequency of 51.2 kHz. The BPF 45a passes the frequency components in a predetermined range (for example, 10 kHz to 15 kHz) of the sampling signal SP(t) and outputs a band-pass signal BPF(t). The absolute value detection unit 47 performs absolute value detection on the band-pass signal BPF(t) and outputs an absolute value signal ABS(t). The BPF 45b passes the frequency components in a predetermined range of the absolute value signal ABS(t) and outputs a band-pass signal BPF(t).

[0092] The frequency shift 42 performs a frequency shift of a specific frequency (fm = 2 kHz) on the band-pass signal BPF(t) output by the BPF 45b. That is, the frequency shift 42 is a multiplier that multiplies the sampling signal SP(t) with the first sampling frequency fs1 = 51.2 kHz and the sine wave signal M(t) with a specific frequency (fm = 2 kHz). This multiplier outputs both the signal component FSh(t) with the upper frequency (Fs1 / 2 + fm = 25.6 kHz + 2 kHz) and the signal component FSl(t) with the lower frequency (Fs1 / 2 - fm = 25.6 kHz - 2 kHz) (output signal).

[0093] That is, the signal component FSh(t) is obtained by shifting the frequency of the band-pass signal BPF(t) upward by a specific frequency (fm = 2 kHz). Also, the signal component FSl(t) is obtained by shifting the frequency of the band-pass signal BPF(t) downward by a specific frequency (fm).

[0094] Similar to the preprocessing unit 40 (Fig. 3) of the first embodiment, the low-pass filter 43 extracts the signal component FSl(t) frequency-shifted downward. The downsampling unit 44 samples the output signal LPF(t) of the low-pass filter 43 at the second sampling frequency of 1.28 kHz and outputs a downsampled signal DNSP(t). The BPF processing unit 46 outputs a preprocessed signal s(t). That is, the preprocessing unit 49 of this modification performs envelope processing after realizing the zoom function. In the case of Fig. 12 (the fifth embodiment), since it is synchronized with the rotation phase θ, a unit using a ratio-order BPF processing unit (not shown) instead of the BPF processing unit 46 of the preprocessing unit 49 is used.

[0095] (2) In the measurement systems 100 (Fig. 1), 101 (Fig. 7), 103 (Fig. 10), and 104 (Fig. 11) of the above embodiments, the random measurement devices 10 (Fig. 1), 11 (Figs. 7, 10, and 11) and the measurement arithmetic units 50 (Fig. 1), 51 (Fig. 7), 52 (Fig. 10), 53 (Fig. 11) were communicably connected, but an integrated configuration may also be used. In this case, the random measurement unit 1 outputs the random measurement vector y, which is serial data, to the receiving unit 55 (Fig. 1), and the receiving unit 55 inputs the random measurement vector y, which is serial data.

[0096] (3) In the above embodiments, the LASSO method was used, but it can be solved using various highly computationally efficient algorithms such as the greedy method, the method based on convex optimization, and the method based on probability propagation.

[0097] (4) In the above embodiments, the discrete-time signal s was subjected to discrete Fourier transform, and the difference between the coefficients x = {x i} estimated by the estimation unit 61 and the Fourier coefficients fk = {fki} was calculated, and it was pre-confirmed that the sum of squares (power difference) was within a predetermined range. Not limited to this, the first power of the sum of squares of the coefficients x = {x i} may be calculated, the second power of the sum of squares of the Fourier coefficients xf = {xf i} may be calculated, and the difference between the first power and the second power may be calculated.

[0098] (5) In each of the above embodiments, the preprocessing unit 40 receives the signal to be measured a(t), and the sampling unit 41 (Fig. 3) outputs the sampling signal SP(t). However, it is not limited to this, and the preprocessing unit 40 may receive the sampling signal SP(t). In any case, the preprocessing unit 40 preprocesses the signal to be measured a(t).

[0099] (6) In the second embodiment, the preprocessing unit 40 (Fig. 3) is provided inside the random measurement device 11 (Fig. 7) and the sequential measurement device 71. However, it is not limited to this, and the preprocessing unit 40 (Fig. 3) may be provided only inside the random measurement device 11, and the signal to be measured a(t) output by the sensor 20 may be input to the sequential measurement unit 73 without providing the preprocessing unit 40 in the sequential measurement device 71. According to this, the DFT calculation unit 74 (Fig. 7) performs DFT calculation on the signal FSl(t) (Fig. 3) that is not downsampled.

Explanation of Reference Numerals

[0100] 1 Random measurement unit (measurement unit) 2 Random matrix setting unit (setting unit) 3 Rotation information acquisition unit 4 Receiving unit 5 Random measurement unit 6 Sequential measurement unit 7 Switch 10, 11, 12, 13 Random measurement device (measurement device) 14 Measurement device 20 Sensor (Doppler vibrometer) 21 Sensor (acceleration sensor) 22 General-purpose sensor 23 Measurement sensor 30 Measurement object 33 Rotating device 40 Preprocessing unit 41 Sampling unit 42 Frequency shift 43 Low-pass filter 44 Downsampling unit 45 Band-pass filter 46 BPF processing unit 47 Absolute value detection unit Measuring and computing device 50, 51, 52, 53 Restoration error computing unit 54 Receiving unit 55 Transmitting unit 56 Anomaly degree computing unit 57 Notification unit 58 Memory unit 59 Control unit (computer) 60 Estimation unit 61 Regularization coefficient setting unit 62 Restoration units 63, 65 x computing unit 64 Restoration unit 65 Random selection unit 67 Switch 68 Frequency correction unit 69 Sequential measuring device 71 Sequential measurement unit 73 DFT computing unit 74 Sampling frequency generator 76 Measuring and computing devices 77, 78, 79 Measurement system (measuring and computing system) 100, 101, 103, 104, 105, 106 Measured signal a(t) Sampling signal SP(t) Pre - processed signal (down - sampled signal) s(t) Random measurement vector y (random measurement value y, second random measurement vector) First random measurement vector y1 First random matrix Φ (random matrix) Regularization coefficient λ Coefficient x Orthogonal basis matrix ψ (orthogonal basis) Fourier basis vector ψf

Claims

1. a pre-processing unit that pre-processes a time-varying signal under test; a random measurement unit that randomly measures the preprocessed signal preprocessed by the preprocessing unit based on a predetermined first random matrix Φ; The pre-processing unit down-samples the signal under test to a signal obtained by shifting the signal under test downward by a specific frequency. A measuring device characterized by:

2. The preprocessing unit includes a bandpass filter that passes the signal under test in a predetermined bandwidth, a multiplier that frequency-shifts the output signal of the bandpass filter up or down by a specific frequency, an LPF that passes only signal components of lower frequencies of the output signal of the multiplier, and a downsampling unit that downsamples the output signal of the LPF.

2. The measuring device according to claim 1 .

3. A rotation information acquisition unit that acquires information on a rotation position or a rotation speed of the rotating device, The random measurement unit performs random measurements in synchronization with the rotational position or the rotational speed.

3. The measuring device according to claim 2.

4. a random measurement unit that randomly measures the preprocessed signal preprocessed by the preprocessing unit based on a predetermined first random matrix Φ; and a transmission unit that transmits a random measurement vector y that is a vector representation of the random measurement values ​​measured randomly and the first random matrix Φ to a measurement and calculation device, wherein the preprocessing unit downsamples the measured signal to a signal that is frequency-shifted downward by a specific frequency; a receiver for receiving the random measurement vector y from the measurement device; and a receiver for computing the random measurement vector y in relation to the first random matrix Φ and basis vector {Ψ ｉ When the n×n orthogonal basis matrix ψ with columns {x} is expressed as the product Φψx of its coefficient x, the regularization coefficient λ0 is determined so that the formula (3) defined in formulas (1) and (2) is minimized. ｉ }; and a measurement calculation device having an estimation unit for estimating A measurement system in which the above components are connected so as to be capable of communicating with each other. [0010] [0025] [0030]

5. A regularization coefficient setting unit that predetermines the regularization coefficient λ 0 in advance based on the random measurement vector y and an arbitrary second random matrix in a first period before the estimation unit estimates the coefficient x so that the regularization coefficient λ 0 becomes a maximum value within a standard deviation of cross-validation at the regularization coefficient λ with the smallest error; A setting unit that sets the second random matrix as the first random matrix Φ in the measurement device; The measurement system of claim 4 further comprising:

6. the signal to be measured during the first period is a signal to be measured by a measurement sensor, In a second period following the first period, the measured signal randomly measured by the random measurement unit is measured by a general-purpose sensor having a frequency characteristic worse than that of the measurement sensor, Further comprising a frequency correction unit that corrects the random measurement vector y output by the random measurement unit during the second period using a frequency characteristic of the general-purpose sensor; The estimation unit estimates coefficients x={xi} of the orthogonal basis matrix ψ using output data of the frequency correction unit during the second period.

6. The measurement system according to claim 5.

7. the first random matrix Φ is a matrix indicating that the signal under test is randomly decimated, The method further includes a regularization coefficient setting unit that determines the regularization coefficient λ0 that is the maximum value within the standard deviation of cross-validation for the regularization coefficient λ with the smallest error.

5. The measurement system according to claim 4.

8. a sequential measurement unit that sequentially measures a time-varying signal under test at a predetermined sampling frequency during a first period; a DFT calculation unit that performs a discrete Fourier transform on the discrete time signal measured by the sequential measurement unit and outputs Fourier coefficients; a pre-processing unit that pre-processes the signal under test or the discrete-time signal; a random measurement value output unit that outputs a first random measurement value that is randomly measured or selected with a predetermined first random matrix Φ using the preprocessed signal preprocessed by the preprocessing unit; A first random measurement vector y1, which is a vector representation of the first random measurement value, is expressed as a first random measurement vector y1 using the first random matrix Φ and the basis vector {Ψ ｉ The orthogonal basis matrix ψ of n×n, whose columns are n, is expressed as a product Φψx of its coefficient x, and the regularization coefficient is λ0. Then, the coefficient x of the orthogonal basis matrix ψ is calculated by multiplying the regularization coefficient λ0 by the product Φψx, so that the formula (6) defined by the formulas (4) and (5) is minimized. ｉ }; and A regularization coefficient setting unit that determines the regularization coefficient λ 0 that is maximum within a standard deviation of cross-validation at a regularization coefficient λ with the smallest error based on the first random measurement vector y 1 and the first random matrix Φ; The pre-processing unit down-samples the signal under test to a signal obtained by shifting the signal under test downward in frequency by a specific frequency, the error is a difference in power between the discrete-time signal and the first random measurement value, calculated using the coefficient x estimated by the estimation unit and the Fourier coefficient; The difference is within a predetermined range A measurement system comprising: [0045] [0050] [006]

9. The power difference is the sum of the squares of the differences between the coefficient x and the Fourier coefficients 9. The measurement system according to claim 8.

10. The power difference is the difference between the power calculated using the coefficient x and the power calculated using the Fourier coefficients.

9. The measurement system according to claim 8.

11. a pre-processing step of pre-processing a time-varying signal under test; A random measurement process for randomly measuring the preprocessed signal preprocessed in the preprocessing process based on a predetermined first random matrix Φ; The pre-processing step down-samples the measured signal by shifting the signal downward by a specific frequency. A measuring method comprising:

12. a pre-processing step of pre-processing a time-varying signal under test; a random measurement step of randomly measuring the preprocessed signal preprocessed in the preprocessing step based on a predetermined first random matrix Φ; The pre-processing step down-samples the measured signal by shifting the signal downward by a specific frequency. A measurement program comprising:

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