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 random measuring device 10 includes a pre-processing unit 40 that pre-processes a signal to be measured a(t) that changes in response to information about a rotational phase θ of a rotating device 30, a random measuring unit 1 that randomly measures a pre-processed signal s(t) pre-processed by the pre-processing unit 40 in synchronization with a rotational position based on a first random matrix Φ, and a transmitting unit that transmits a random measurement vector y that is a vector representation of a random measurement value measured at random, and the first random matrix Φ to a measurement calculation apparatus 50. The measurement calculation apparatus 50 includes an estimation unit 61 that uses the LASSO technique to estimate a coefficient x={xi} of an n×n orthogonal basis matrix ψ whose columns are a basis vector {Ψi} based on the random measurement vector y. The random measuring device and the measurement calculation apparatus are communicatively connected to each other.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 measuring the characteristics of a rotating device, for example.

Background Art

[0002] Rotating devices will inevitably fail due to material defects, fatigue, aging, etc. When a failure occurs, it leads to equipment downtime and economic losses. Therefore, it is important to perform fault diagnosis on rotating devices and keep them in a healthy state. Fault diagnosis of rotating devices is carried out 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 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. Also, Patent Document 1 discloses a measurement data providing service system that assigns an ID to a sensor, centrally manages it 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 out (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 capable of reducing 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 measuring unit that randomly measures the preprocessed signal based on a predetermined first random matrix Φ, wherein the preprocessing unit downsamples an envelope signal indicating an envelope of a sampling signal obtained by sampling the signal to be measured.

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]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8A

Figure 8B

Figure 8C

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

Figure 26

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 figure only schematically shows to the extent that the present invention can be sufficiently understood. Therefore, the present invention is not limited only to the illustrated examples. Also, in each figure, 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 a measurement system which is an embodiment of the present invention. The measurement system 100 measures the characteristics (e.g., vibration) of the rotating device 30 with the sensor 20, and the random measurement device 10 and the measurement calculation device 50 are communicably connected. The rotating device 30 is, for example, a bearing and includes rotating electrical machines such as motors and generators. The sensor 20 is, for example, an acceleration sensor and detects the vibration of the rotating device 30. Also, the rotation angle sensor 35 outputs a rotation phase θ indicating the rotation position of the rotating device 30.

[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) in synchronization with the rotation phase θ. 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, a rotation information acquisition unit 3, and a reception 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 a measurement target facility for inspecting a measurement target. The measurement target facility 150 includes a rotating device 30 as a measurement target, a motor 32, a sensor 20, and a rotation angle sensor 35. The rotating device 30 is, for example, a bearing having an inner ring 30a and an outer ring 30b. The rotating device 30 has an outer ring 30b with a scratch as the evaluation target. Note that for comparison, there are rotating devices 30 with large scratches and those with small scratches. The inner ring 30a of the rotating device 30 is rotated by the motor 32. The rotation angle sensor 35 detects the rotation position of the inner ring 30a and outputs the rotation phase θ. The sensor 20 is an acceleration sensor that detects the vibration of the rotating device 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 includes a sampling unit 41, a BPF (Band Pass Filter) 42, an absolute value detection unit 43, an LPF (Low Pass Filter) 44, a downsampling unit 45, and an inverse BRF (Band Rejection Filter) processing unit (order ratio inverse BRF processing unit 46).

[0016] The sampling unit 41 digitally converts the measured signal a(t) at a first sampling frequency fs1 (for example, fs1 = 25.6 kHz) and outputs a sampling signal SP(t). The BPF 42 passes frequency components in a predetermined range (for example, 1 kHz to 10 kHz) of the sampling signal SP(t) and outputs a band-pass signal BPF(t). The absolute value detection unit 43 performs absolute value detection on the band-pass signal BPF(t) and outputs an absolute value signal ABS(t). The LPF 44 blocks the high-frequency components of the detected signal ABS(t) and outputs a low-pass signal LPF(t) as an envelope signal. The downsampling unit 45 samples the low-pass signal LPF(t) at a second sampling frequency fs2 (for example, fs2 = 1.28 kHz) lower than the first sampling frequency fs1 (for example, fs1 = 25.6 kHz) and outputs a downsampled signal DNSP(t). The order ratio inverse BRF processing unit 46 is a filter processing unit that passes a specific frequency component (specific order ratio component) corresponding to the order ratio and outputs a preprocessed signal s(t). The specific frequency (specific order) of this specific frequency component (specific order ratio component) corresponds to the rotational position (rotational phase θ) or the rotational speed. Note that the order ratio inverse BRF processing unit 46 may alternatively be provided with a BPF processing unit (filter processing unit) that passes a band including a specific frequency component (specific order ratio component).

[0017] Figures 4 and 5 are diagrams showing an example of the waveforms of each part in the preprocessing unit. Figure 5 shows a larger scratch on the outer ring 32b than in Figure 4.

[0018] The top waveforms in FIGS. 4 and 5 are the sampling signal SP(t) obtained by the sampling unit 41 sampling the signal to be measured a(t). The second row is the band-pass signal BPF(t). The third row is the low-pass signal LPF(t) that has passed through the absolute value detector 43 and the LPF 44. The low-pass signal LPF(t) represents the envelope of the output signal of the absolute value detector 43. The fourth row is the downsampling signal DNSP(t), and the fifth row is the preprocessing signal s(t) after the order ratio inverse BRF processing.

[0019] Returning to the description of FIG. 1, the random measurement unit 1 synchronizes the preprocessing signal s(t) with the rotation phase θ and outputs (transmits) to the measurement arithmetic device 50 the signal of the random measurement vector y = Φs obtained by randomly sampling according to the first random matrix Φ in vector form. Here, the measurement period is divided into a parameter setting period (the first period) for setting measurement parameters (for example, the regularization coefficient λ described later) and a measurement period (the second period) after the parameter setting.

[0020] FIG. 6 is a diagram for explaining the relationship between the parameter setting period (the first period T1) and the measurement period (the 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 the measurement interruption period.

[0021] Let the random measurement vector measured in the first period T1 be the first random measurement vector y1 = Φs, and the random measurement vector (the second random measurement vector) measured in the second period T2 be y = Φs. Here, the first random matrix Φ includes a matrix Φr indicating randomly decimating the columns (discrete-time signal s) of all time-series signals synchronized with the rotation phase θ of the preprocessing signal s(t), and a matrix Φrsu indicating performing multiple measurements to randomly set the measurement start timing of the discrete-time signal s, etc. The matrix Φ indicating random sampling r indicates performing measurement to randomly decimate the columns (discrete-time signal s) of all time-series signals obtained by equally spacing the preprocessing signal s(t).

[0022] The matrix Φrsu measures data of M points at a constant angular frequency ω rsu (ω rsu << sampling angular frequency ωs) or at a constant frequency f rsu in one measurement. As a result, the number of samples taken by the random measurement unit 1 of the preprocessing signal s(t) is reduced compared to the number of discrete-time signals s. The random measurement unit 1 can be manufactured at a lower cost by sampling the preprocessing signal s(t) in synchronization with the rotation phase θ and outputting all the time-series signal columns (discrete-time signals s). p 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, the second random matrix Φ0 is used as an initial value, and the first random matrix Φ is obtained by updating the second random matrix Φ0. The rotation information acquisition unit 3 detects the rotation position of the rotating device 30 and outputs it to the random measurement unit 1 as a signal of the rotation phase θ. The receiving unit 4 receives the update data (first random matrix Φ) of the random matrix setting unit 2 from the measurement arithmetic unit 50.

[0023]

[0024] In the second period T2 (Fig. 6), the measurement arithmetic unit 50 restores the discrete-time signal s from the random measurement value (random measurement vector y = Φs) received from the random measurement device 10. That is, the measurement arithmetic unit 50 restores all the data (discrete-time signal s) from the 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 the rotation phase θ as a variable. Note that one period of the Fourier basis vector corresponds to one rotation of the rotating device 30.

[0025] ​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.

[0026] 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 to λ0, the coefficient x = {x i} is estimated so that the following equation (1) is minimized.

Equation

[0027] Here, the norms in the mathematical expressions are defined by the following equations (2) and (3).

Equation

Equation

[0028] 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 an error.

[0029] Before estimating the coefficient x of the n×n orthogonal basis matrix ψ in the second period T2, 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 at the regularization coefficient λ with the least error. At this time, for the first random matrix Φ, the initial value (the 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.

[0030] 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.

[0031] 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.

[0032] FIG. 7 is a diagram for explaining the difference in the number of samples of the preprocessing signal s(t) depending on the high or low rotational speed. The horizontal axis represents time t, and the vertical axis in the following figure represents the preprocessing signal s(t). The preprocessing 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 preprocessing signal s(t) is sampled in synchronization with the rotational phase are indicated by white circles (○). For example, in the following figure of FIG. 7, white circles (○) are added 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.

[0033] Here, a phenomenon that occurs once per rotation as one cycle is defined as a rotation primary component, and n times that is defined as a rotation n-th component. An analysis performed with the X-axis representing the order and the Y-axis representing the magnitude of the vibration noise of the order component is called "rotation order ratio analysis".

[0034] FIG. 8A 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). Further, FIG. 8B is a diagram showing the time change of the rotation phase of the rotating device. The horizontal axis is time t, and the vertical axis is the rotation phase θ(t). Here, it is assumed that the preprocessed signal s(t) is a sine wave signal whose frequency gradually increases. Black dots (●) are attached to a plurality of measurement points a, b, c, d of the preprocessed signal s(t) and the rotation phase θ(t).

[0035] In FIG. 8B, at time t = 0, the rotation phase θ(0) = 0, and the rotation phase θ(t) monotonically increases with the passage of time (measurement points a → b → c → d). For example, at point b (FIG. 8A), since it is before the third cycle, the rotation phase is less than (360×4)°. At point c (FIG. 8A), since it is before the fifth cycle, the rotation phase is more than (360×4)°. At point d (FIG. 8A), it is after the sixth cycle, and the rotation phase is between (360×4)° and (360×8)°.

[0036] FIG. 8C is a diagram showing the relationship between the measurement signal and the rotation phase. The horizontal axis is the rotation phase θ, and the vertical axis is the preprocessed signal s(θ). Between c - d, although the time T3 (FIG. 8A) is short, the rotation phase width Θ1 is expressed as long. In other words, as shown in FIG. 8C, if the rotation phase θ is made a variable, even if the rotation speed of the rotating device 30 changes, the preprocessed signal s(θ) can be evaluated as a sine wave.

[0037] FIG. 9 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 is changed. Thereby, the measurement operation device 50 pre-determines parameters (regularization coefficient λ and first random matrix Φ) in the first period T1 (FIG. 6) and starts measurement in the second period T2 (FIG. 6). Also, a random matrix Φ = Φ0 is set (stored) in the random matrix setting unit 2 in advance.

[0038] 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). Also, the random measurement device 10 receives a signal of the rotation phase θ(t) from the rotation device 30. Thereby, the random measurement device 10 acquires the discrete-time signal s. The random measurement device 10 calculates a random measurement vector y = Φs using the pre-sampled 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 operation device 50 (step S3). The measurement operation device 50 receives the random measurement vector y (step S4) and determines the regularization coefficient λ = λ0 to be 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) may use the random matrix Φ = Φ0, but may appropriately correct the first random matrix Φ and then determine the regularization coefficient λ0.

[0039] After the process of step S5, the measurement operation device 50 transmits the corrected first random matrix Φ in order to set the appropriately corrected first random matrix Φ in the random measurement device 10 (step S6). The random measurement device 10 receives the first random matrix Φ and re-sets it to the first random matrix Φ received from the second random matrix Φ0 set in the random matrix setting unit 2 (step S7). Thereby, the random measurement device 10 completes the preparation for starting measurement.

[0040] In the second period T2, 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. Also, the random measurement device 10 is receiving the signal of the rotation phase θ(t) from the rotation device 30. 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 (step S13).

[0041] Figs. 10 and 11 are diagrams showing the coefficients x = {x i} estimated by the estimator 61. The vertical axis represents the coefficient x [m / s 2 , and the horizontal axis represents the order. The maximum value of the vertical axis in Fig. 10 is 0.15 [m / s 2 , and the maximum value of the vertical axis in Fig. 11 is 6 [m / s 2 . Also, Fig. 11 shows the characteristics of a sample with a larger scratch on the outer ring 32b than in Fig. 10. For the sample with a small scratch (Fig. 10), the rotational first-order component X1 = 0.08647 [m / s 2 , and the rotational second-order component X2 = 0.0998 [m / s 2 . Also, for the sample with a large scratch (Fig. 11), the rotational first-order component X1 ≈ 0.4 [m / s 2 , and the rotational second-order component X2 = 4.3741 [m / s 2 . That is, in the sample with a small scratch (Fig. 10), the rotational first-order component and the rotational second-order component appear to be of the same degree, but in the sample with a large scratch (Fig. 11), the rotational second-order component has increased significantly more than the rotational first-order component.

[0042] Figures 12 and 13 are diagrams showing the analysis of the downsampling signal DNSP(t) by order ratio. The vertical axis represents the acceleration amplitude [m / s 2 , and the horizontal axis represents the order. The maximum value of the vertical axis in Figure 12 is 0.125 [m / s 2 , and the maximum value of the vertical axis in Figure 13 is 4 [m / s 2 . The same results as in Figures 10 and 11 are obtained.

[0043] As described above, according to the measurement system 100 of the present embodiment, downsampling is performed by the preprocessing unit 40 and random sampling is performed by the random measurement unit 1, so that the number of samples is reduced in an overlapping manner. Therefore, the number of data of the random measurement vector y transmitted from the random measurement device 10 to the measurement arithmetic unit 50 is extremely reduced.

[0044] (Second Embodiment) In the first embodiment, it is 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 (Figure 9)). In this embodiment, the error is calculated by the difference between the sum of products of powers calculated by CS (Compressed Sensing) and the sum of products of powers calculated by DFT (Discrete Fourier Transform) operation.

[0045] Figure 14 is a configuration diagram of a measurement system according to the second embodiment of the present invention. The measurement system 101 is configured by communicably connecting a random measurement device 11, a sequential measurement device 70, and a measurement arithmetic unit 51.

[0046] The random measurement device 11 includes the preprocessing unit 40 described above, a random measurement unit 1 as a random measurement value output unit, and a rotation information acquisition unit 3. The random measurement unit 1 randomly acquires the preprocessing signal s(t) preprocessed by the preprocessing unit 40 in synchronization with the rotation phase θ. Note that the acquisition timing for random acquisition may or may not be synchronized with the clock of the second sampling frequency fs2 of the downsampling unit 45 (Figure 3) of the preprocessing unit 40.

[0047] The sequential measurement device 70 includes a preprocessing unit 40, a sequential measurement unit 73, a DFT calculation unit 74, and a PLL 75. The PLL (Phase Locked Loop) 75 generates a phase synchronization signal with a sampling angular frequency ω s = Nω that is an integer multiple of the input angular frequency ω = dθ / dt by inputting a signal of the rotational phase θ. The generated phase synchronization signal is also used as the clock of the second sampling frequency fs2 of the downsampling unit 45 (FIG. 3) of the preprocessing unit 40. The sequential measurement unit 73 sequentially measures the preprocessed signal s(t) preprocessed by the preprocessing unit 40 at a sampling angular frequency ωs (ωs = 2πfs2) synchronized with the rotational phase θ, and outputs a discrete-time signal s. In particular, when the matrix Φ rsu indicates a random start, the sampling angular frequency ωs = Nω rsu is obtained.

[0048] The DFT (Discrete Fourier Transform) calculation unit 74 performs a discrete Fourier transform on the discrete-time signal s and outputs the calculation result (Fourier coefficients xf = {xf i}) to the measurement calculation device 50. The sequential measurement device 70 is different from the random measurement device 10 (FIG. 1) in that it does not perform random measurements and the sampling angular frequency ωs = Nω rsu is high.

[0049] The measurement calculation device 51 checks the Fourier coefficients xf = {xf i} in the first period T1 (FIG. 6), makes a sparsity determination, and sets a parameter (regularization coefficient λ). Specifically, in the first period T1, the measurement calculation device 50 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 calculation device 50 sets a parameter (regularization coefficient λ).

[0050] Also, in the second period T2, similar to the measurement and calculation device 50 (Fig. 1), the measurement and calculation 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.

[0051] The measurement and calculation device 51 is a PC, and by executing a measurement and calculation 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.

[0052] 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 (7)). The restoration error calculation unit 54 checks 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.

[0053]

Equation

[0054] 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.

[0055] Figs. 15 and 16 are diagrams showing the POA of acceleration in terms of order. The vertical axis is the POA [m / s 2where the horizontal axis is the order. Note that POA (Partial Over-All) is the sum (product sum) of powers within a predetermined spectral interval. Note that "Over-All" is the sum (product sum) of powers of all frequencies. Also, the parameters in FIGS. 15 and 16 are of three types: CS (white circle "○"), DFT (diamond "◇"), and FFT (square "□"). Here, DFT is calculated with a frame length of 10 seconds at the second sampling frequency (e.g., 1.28 kHz), and FFT is different in that it divides a 10-second interval into 10 1024 frames = 1024 frames in length and averages the total frame length.

[0056] For a sample with small damage (FIG. 15), the rotational second-order POA by CS is CS2 = 0.100017, and the second-order POA by FFT is FFT2 = 0.13381. Also, for a sample with large damage (FIG. 16), the rotational second-order POA by CS is CS2 = 4.3847, and the rotational second-order POA by FFT is FFT2 = 5.59547. Also, for a sample with small damage (FIG. 15), the rotational first-order POA is slightly less than the rotational second-order POA. However, for a sample with large damage (FIG. 16), since the rotational second-order POA is significantly larger, the rotational first-order POA is much less than the rotational second-order POA.

[0057] (Third Embodiment) In the first and second embodiments, the random measurement unit 1 randomly samples in synchronization with the rotational phase θ, but it is also possible to randomly acquire the measured signal s(t) at a predetermined sampling frequency fs or sampling angular frequency ωs.

[0058] FIG. 17 is a configuration diagram of a measurement system according to the third embodiment of the present invention. The measurement system 102 includes a random measurement device 11, a sequential measurement device 71, and a measurement arithmetic unit 52. The random measurement device 11 differs from the random measurement device 11 (FIG. 14) of the second embodiment in that it does not have the rotation information acquisition unit 3 and has a preprocessing unit 48 instead of the preprocessing unit 40. That is, the random measurement unit 1 drives the preprocessing signal s(t) at a predetermined sampling frequency fs or sampling angular frequency ωs without synchronizing with the rotation phase θ. As a result, the random measurement unit 1 randomly acquires the preprocessing signal s(t) and outputs a random measurement vector y = Φs.

[0059] FIG. 18 is a configuration diagram of the preprocessing unit 48 used in the measurement system 102 according to the third embodiment of the present invention. The preprocessing unit 48 is similar to the preprocessing unit 40 of the above embodiment in that it includes a sampling unit 41, a BPF 42, an absolute value detection unit 43, an LPF 44, and a downsampling unit 45. However, the preprocessing unit 48 differs from the preprocessing unit 40 in that it does not include the order ratio inverse BRF processing unit 46. That is, the downsampling signal DNSP(t) is output as the preprocessing signal s(t).

[0060] Returning to the description of FIG. 17, the sequential measurement device 71 includes a sequential measurement unit 73 and a DFT calculation unit 74, but differs from the sequential measurement device 70 (FIG. 14) of the above embodiment in that it has a sampling frequency generator 76 instead of the PLL 75 (FIG. 1) and has a preprocessing unit 48 instead of the preprocessing unit 40. That is, the sequential measurement unit 73 sequentially measures the preprocessing signal s(t) at the sampling frequency fs or sampling angular frequency ωs generated by the sampling frequency generator 76. Here, the sequential measurement unit 73 is synchronized with a second sampling frequency fs2 that drives the downsampling unit 45 (FIG. 18) of the preprocessing unit 48.

[0061] The measurement calculation device 52 includes a restoration error calculation unit 54, an abnormality degree calculation 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 calculation device 50 of the first embodiment. However, the measurement calculation device 52 differs from the measurement calculation device 51 (FIG. 14) of the second embodiment in that it includes a random selection unit 67 and a switch 68.

[0062] In the first period T1, 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. 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 in which the random measurement values are vectorially represented. The switch 68 is a one-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. In this regard, it is different from the second embodiment in which the rotation phase θ is the variable.

[0063] 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 the random measurement unit 1 also outputs the first random measurement vector y1 = Φs, but is blocked by the switch 68.

[0064] 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 embodiment, the restoration unit 63 restores the discrete-time signal s.

[0065] FIG. 19 is a configuration diagram of another preprocessing unit used in the measurement system 102 according to the third embodiment of the present invention. The preprocessing unit 49 is used in place of the preprocessing unit 48 (Fig. 17). Similar to the preprocessing unit 48 of the said embodiment, the preprocessing unit 49 includes a sampling unit 41, a BPF 42, an absolute value detection unit 43, an LPF 44, and a downsampling unit 45. However, the preprocessing unit 49 is different in that it includes a characteristic frequency filter 47 after the downsampling unit 45. The characteristic frequency filter 47 is a filter that passes frequency components (components of the characteristic frequency) with peaks in the frequency domain. This characteristic frequency is measured in advance during the first period T1 (Fig. 6). Note that in the characteristic frequency filter 47, an inverse BRF process or a BPF process in terms of the number of frequencies is performed.

[0066] (Fourth Embodiment) Fig. 20 is a configuration diagram of the measurement system according to the fourth embodiment of the present invention. Similar to the measurement system 100 (Fig. 1) of the said embodiment, the measurement system 103 includes a random measurement device 10 and a measurement arithmetic unit 53. However, the random measurement unit 1 of the random measurement device 10 is connected to a general-purpose sensor 21 instead of the sensor 20 (Fig. 1). The general-purpose sensor 21 is, for example, a general-purpose sensor made of MEMS, and is inexpensive but has poor frequency characteristics compared to when a measurement sensor is used as the sensor 20.

[0067] Fig. 21 is a diagram showing the frequency characteristics of a general-purpose microphone and a measurement microphone. The horizontal axis represents frequency [Hz], and the vertical axis represents decibel. The solid line represents the measurement microphone, and the dashed line represents the general-purpose microphone made of MEMS. The solid line and the dashed line are 0 decibel at the reference frequency of 1 kHz. The measurement microphone maintains flat frequency characteristics from about 20 Hz to about 20 kHz. In contrast, the general-purpose microphone made of MEMS has a reduced output at low frequencies from 20 Hz to about 200 Hz.

[0068] The measurement and calculation device 53 differs from the measurement and calculation device 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 a relatively low frequency of about 20 Hz to 200 Hz, making the frequency characteristics combined with the general-purpose sensor 21 comparable to those of the measurement sensor. The frequency correction unit 69 outputs correction data to the estimation unit 61 and the regularization coefficient setting unit 62.

[0069] (Fifth Embodiment) Fig. 22 is a configuration diagram of the measurement system according to the fifth embodiment of the present invention. Similar to the measurement system 101 (Fig. 14) of the fourth embodiment, the measurement system 104 includes a random measurement device 12, a measurement and calculation device 59, and a sequential measurement device 70. The random measurement device 12 further includes a switch 8, which is different from the random measurement device 11 (Fig. 14) in that the switch 8 switches to either the general-purpose sensor 21 or the measurement sensor 22. The measurement and calculation device 59 differs from the measurement and calculation device 51 (Fig. 14) in that it further includes a frequency correction unit 69 and a switch 9. Also, the sequential measurement device 70 connects the measurement sensor 22 instead of the sensor 20 (Fig. 14).

[0070] The switches 8 and 9 are two-contact switches that connect either terminal a or b to terminal c. The switches 8 and 9 are connected to terminal b during the first period T1 (Fig. 6) and to terminal a during the second period T2 (Fig. 6). That is, the switch 8 connects the measurement sensor 22 and the random measurement unit 1 during the first period T1, and connects the general-purpose sensor 21 and the preprocessing unit 40 during the second period T2. The switch 9 connects the random measurement unit 1 to the estimation unit 61 and the regularization coefficient setting unit 62 during the first period T1, and connects the frequency correction unit 69 to the estimation unit 61 and the regularization coefficient setting unit 62 during the second period T2.

[0071] (Sixth Embodiment) In the fifth embodiment, the frequency correction unit 69 is provided inside the measurement and calculation device 59, but it can also be provided inside the preprocessing unit 40.

[0072] FIG. 23 is a configuration diagram of a measurement system according to a sixth embodiment of the present invention. The measurement system 105 includes a random measurement device 13, a measurement arithmetic unit 51, and a sequential measurement device 70, similar to the measurement system 101 (FIG. 14) of the fifth embodiment. The random measurement device 13 is different from the random measurement device 11 (FIG. 14) in that it includes a switch 8 and a preprocessing unit 49 instead of the preprocessing unit 40. The switch 8 switches to either the general-purpose sensor 21 or the measurement sensor 22, similar to the random measurement device 12 (FIG. 23).

[0073] FIG. 24 is a configuration diagram of the preprocessing unit 49 used in the measurement system according to the sixth embodiment of the present invention. The preprocessing unit 49 is common to the preprocessing unit 40 of the first embodiment in that it includes a sampling unit 41, a BPF 42, an absolute value detection unit 43, an LPF 44, a downsampling unit 45, and an inverse BRF processing unit (order ratio inverse BRF processing unit 46). However, the preprocessing unit 49 is different in that a frequency correction unit 69 is inserted between the sampling unit 41 and the BPF 42.

[0074] (Comparative Example) In each of the above embodiments, the preprocessing signal s(t) was restored by compressive sampling (CS) in synchronization with the rotation phase of the rotating device 30. However, the preprocessing signal s(t) may be restored by DFT conversion without performing compressive sampling.

[0075] FIG. 25 is a configuration diagram of a measurement system according to a comparative example of the present invention. The measurement system 106 is configured such that the measuring device 14 and the measurement arithmetic unit 79 are communicably connected. The measuring device 14 includes a preprocessing unit 48 and a sequential measurement unit 5. The preprocessing unit 48 preprocesses the measured signal a(t) of the sensor 20 and outputs a preprocessed signal s(t). The sequential measurement unit 5 sequentially measures the preprocessed signal s(t) at a predetermined sampling time and outputs a discrete-time signal s. That is, the measuring device 14 is different from the random measuring device 11 of the second embodiment in both that it does not sample randomly and that it is not synchronized with the rotational phase θ(t) from the rotating device 30.

[0076] The measurement arithmetic unit 79 includes a receiving unit 55, an x arithmetic unit 64, and a restoration unit 65. The receiving unit 55 receives the discrete-time signal s from the measuring device 14. The x arithmetic unit 64 calculates 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 arithmetic unit 64 performs a discrete Fourier transform on the discrete-time signal s. The restoration unit 65 restores the discrete-time signal s = ψf·xf using the Fourier basis vector ψf and the Fourier coefficient xf.

[0077] Also, since the sequential measurement unit 5 sequentially acquires the preprocessed signal s(t) at every predetermined sampling time, the measurement arithmetic unit 79 can perform a fast Fourier transform. However, in the above embodiment, since the preprocessed signal s(t) is randomly sampled, a discrete Fourier transform cannot be performed. However, in the measurement arithmetic units 50 (FIG. 1) and 51 (FIG. 14) of the above embodiments, by solving the L1 regularization by LASSO (Least Absolute Shrinkage and Selection Operator), the coefficient x of the n×n orthogonal basis matrix ψ is made sparse.

[0078] (Modification example) The present invention is not limited to the above embodiments, and modifications can be made 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 first embodiment, only envelope processing was performed, but a zoom function can be added. The preprocessing unit 78 shown in Fig. 26 includes a sampling unit 41, a BPF 42a, an absolute value detector 43, a BPF 42b, a frequency shift 77, an LPF 44, a downsampling unit 45, and a BPF processing unit (order ratio BPF processing unit 66).

[0079] The sampling unit 41 samples the signal to be measured a(t) at the first sampling frequency of 51.2 kHz. The BPF 42a 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 detector 43 performs absolute value detection on the band-pass signal BPF(t) and outputs an absolute value signal ABS(t). The BPF 42b passes the frequency components in a predetermined range of the absolute value signal ABS(t) and outputs a band-pass signal BPF(t). The frequency shift 77 performs a frequency shift corresponding to a specific order ratio (corresponding to the 40th component of a rotational speed of 3000 r / min, fm = 2 kHz) on the band-pass signal BPF(t) output by the BPF 42b. That is, the frequency shift 77 is a multiplier that multiplies the sampling signal SP(t) with the first sampling frequency fs1 = 51.2 kHz by a sine wave signal M(t) with a specific frequency (fm = 2 kHz). This multiplier outputs signals (output signals) of 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).

[0080] That is, the signal component FSh(t) is the band-pass signal BPF(t) frequency-shifted upward by a specific frequency (fm = 2 kHz). Also, the signal component FSl(t) is the band-pass signal BPF(t) frequency-shifted downward by a specific frequency (fm).

[0081] Similar to the preprocessing unit 40 (Fig. 3) of the first embodiment, the LPF 44 extracts the signal component FSl(t) frequency-shifted downward. The downsampling unit 45 samples the output signal LPF(t) of the LPF 44 at the second sampling frequency of 1.28 kHz and outputs a downsampled signal DNSP(t). The order ratio BPF processing unit 66 outputs a preprocessed signal s(t). That is, the preprocessing unit 78 of this modification performs envelope processing after realizing the zoom function. In the case of Fig. 17 (third embodiment), since it is not synchronized with the rotation phase θ, a BPF processing unit (not shown) is used instead of the order ratio BPF processing unit 66 of the preprocessing unit 78.

[0082] (2) In the measurement system 100 (Fig. 1) of each of the above embodiments, the random measurement device 10 and the measurement arithmetic unit 50 were communicably connected, but they may be integrally configured. In this case, the random measurement unit 1 outputs the random measurement vector y, which is serial data, to the receiving unit 55, and the receiving unit 55 inputs the random measurement vector y, which is serial data.

[0083] (3) In the above embodiment, 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.

[0084] (4) In the random measurement device 10 of the above embodiment, random sampling was performed in synchronization with the signal of the rotation phase θ indicating the rotation position of the rotating device 30. However, even with the rotation speed, the rotation position can be calculated by performing unwrapping processing and then integration processing. That is, the rotation information acquisition unit 3 acquires information on the rotation position or rotation speed of the rotating device 30, and the random measurement device 10 performs random sampling in synchronization with the information on the rotation position or rotation speed of the rotating device 30.

[0085] (5) In the second embodiment, the discrete-time signal s was subjected to discrete Fourier transform, and the coefficient x = {x i} is calculated, and it is confirmed in advance that the sum of squares (power difference) is within a predetermined range. Not limited to this, the first power of the sum of squares of the coefficient x = {x i} is calculated, and the second power of the sum of squares of the Fourier coefficient xf = {xf i} is calculated, and the difference between the first power and the second power may be calculated.

[0086] (6) In each of the above embodiments, the preprocessing unit 40 receives the measured signal a(t), and the sampling unit 41 (FIG. 3) outputs the sampling signal SP(t). Not limited to this, the preprocessing unit 40 may receive the sampling signal SP(t). In any case, the preprocessing unit 40 preprocesses the measured signal a(t).

[0087] (7) In the second embodiment, the preprocessing unit 40 (FIG. 14) is provided inside the random measurement device 11 (FIG. 14), and the sequential measurement device 70 is not provided with the preprocessing unit 40. Not limited to this, the preprocessing unit 40 may be provided between the random measurement device (having the same configuration as the random measurement device 10 (FIG. 1)) and the sequential measurement device 70, and the sensor 20. According to this, the DFT calculation unit 74 (FIG. 14) performs DFT calculation on the preprocessed signal s(t) that has undergone preprocessing.

Explanation of Signs

[0088] 1 Random measurement unit (measurement unit) 2 Random matrix setting unit (setting unit) 3 Rotation information acquisition unit 4 Receiving unit 5 Sequential measurement unit 8, 9 Switch 10, 11, 12, 13 Random measurement device 14 Measurement device 21 General-purpose sensor 22 Measurement sensor 30 Rotation device (bearing) 40, 48, 49, 78 Preprocessing unit 41 Sampling unit 42 Band-pass filter 43 Absolute value detection unit 44 LPF 45 Downsampling section 46 Inverse BRF processing section (filter processing section) 47 Characteristic frequency filter 50, 51, 52, 53, 59, 79 Measurement and calculation device 54 Restoration error calculation section 55 Receiver 56 Transmitter 57 Abnormality degree calculation section 58 Notification section 60 Control section (computer) 61 Estimation section 62 Regularization coefficient setting section 63, 65 Restoration section 64 x calculation section 66 Order ratio BPF processing section 67 Random selection section 68 Switch 69 Frequency correction section 73 Sequential measurement section 74 DFT calculation section 75 PLL 77 Frequency shift 100, 101, 102, 103, 104, 105, 106 Measurement system (measurement and calculation system) 150 Equipment under measurement a(t) Measured signal SP(t) Sampling signal LPF(t) Low-pass signal (envelope signal) DNSP(t) Downsampled signal s(t) Preprocessed signal s Discrete-time signal θ Rotation phase (rotation position) y Random measurement vector (random measurement value y, second random measurement vector) y1 First random measurement vector Φ First random matrix λ Regularization coefficient x Coefficient ψ Orthogonal basis matrix (orthogonal basis) ψf Fourier basis vector

Claims

1. a pre-processing unit that pre-processes a time-varying signal under test; a 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 an envelope signal that indicates an envelope of a sampled signal obtained by sampling the signal under measurement. A measuring device characterized by:

2. A rotation information acquisition unit that acquires information on a rotation position or a rotation speed of the rotating device, The pre-processing unit further includes a filter processing unit that passes a specific frequency component corresponding to the rotational position or the rotational speed of the downsampled signal.

2. The measuring device according to claim 1 .

3. The present invention relates to a measurement device that includes a pre-processing unit that pre-processes a time-varying signal under test, a measurement unit that randomly measures the pre-processed signal pre-processed by the pre-processing 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 at random and the first random matrix Φ to a measurement and calculation device, wherein the pre-processing unit down-samples an envelope signal that indicates an envelope of the signal under test, 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]

4. 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 3 further comprising:

5. 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 preprocessed by the preprocessing unit is measured by a general-purpose sensor having a frequency characteristic worse than that of the measurement sensor, A frequency correction unit is further provided to correct the random measurement vector y output by the 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.

5. The measurement system according to claim 4.

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 preprocessed by the preprocessing unit is measured by a general-purpose sensor having a frequency characteristic worse than that of the measurement sensor, The pre-processing unit pre-processes a corrected signal obtained by correcting a measurement signal measured by the general-purpose sensor using a frequency characteristic of the general-purpose sensor, The estimation unit estimates coefficients x={xi} of the orthogonal basis matrix ψ using the measured signal whose frequency characteristics have been corrected during the second period.

5. The measurement system according to claim 4.

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.

4. The measurement system according to claim 3.

8. a sequential measurement unit that sequentially measures a time-varying signal under test at a first sampling frequency or a sampling angular 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 according to a predetermined 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 vector using the 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 random matrix Φ; the pre-processing unit down-samples an envelope signal indicating an envelope of the signal under measurement, the predetermined first sampling frequency is equal to a second sampling frequency when the pre-processing unit downsamples, 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 pre-processing unit further includes a feature frequency filter that passes a feature frequency component measured in the first period for the downsampled signal. The measurement system according to claim 8 .

10. The power difference is the sum of the squares of the differences between the coefficient x and the Fourier coefficients 10. The measurement system according to claim 8 or 9.

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

10. The measurement system according to claim 8 or 9.

12. 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 includes down-sampling an envelope signal indicative of an envelope of the signal under test. A measuring method comprising:

13. 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 includes down-sampling an envelope signal indicative of an envelope of the signal under test. A measurement program comprising:

Images