Measurement system, measurement calculation device, measurement calculation method, and measurement calculation program

Abstract

To increase the rate of restoration of an original signal while reducing measurement data.SOLUTION: A measurement system includes: a sequential measurement instrument 70 for sequentially measuring a measured signal s(t) that changes in response to a rotational position θ of a rotating electric machine 30 at a predetermined sampling angular frequency ωs during a first period; a DFT calculation unit 74 for performing a discrete Fourier transform on a discrete-time signal s measured by the sequential measurement instrument 70 and outputting a Fourier coefficient xf; a random measurement instrument 10 for outputting a first random measurement value that is randomly measured with a predetermined random matrix Φ using the measured signal s(t); an estimation unit 61 for estimating a coefficient x of an orthogonal basis matrix ψ when a first random measurement vector y1 that is a vector representation of the first random measurement value is expressed as a product Φψx of the random matrix Φ and the orthogonal basis matrix ψ and its coefficient x, and a regularization coefficient is λ0; and a regularization coefficient setting unit 62 for determining the regularization coefficient λ=λ0 based on the first random measurement vector y1 and the random matrix Φ.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a measurement system, a measurement and calculation device, a measurement and calculation method, and a measurement and calculation program, and relates to, for example, a measuring device that measures the characteristics of a rotating machine. [Background technology]

[0002] Rotating machinery inevitably fails due to material defects, fatigue, aging, etc. Failures lead to equipment downtime and economic losses. Therefore, it is important to diagnose rotating machinery and keep it in good condition. Fault diagnosis of rotating machinery is performed using various sensing methods.

[0003] For example, Non-Patent Document 1 discloses a technology that combines compressed sensing technology with 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 technology that can accurately restore a signal from much less measurement data than is normally required, if it satisfies the conditions that the measurement data has sparsity with respect to a certain basis (e.g., Fourier basis) and that the basis is incoherent (random sampling is performed). As a result, the technology in Non-Patent Document 1 reduces the measurement data required for monitoring. Furthermore, Patent Document 1 discloses a measurement data providing service system that assigns IDs to sensors, centrally manages them in a server system, and performs temperature compensation and linearity compensation processing according to the situation. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Yoshimoto Kato, "Propeller Fault Diagnosis Using Sub-Nyquist Sampling and Compressive Sensing", 19th Symposium on Evaluation and Diagnosis, Japan Society of Mechanical Engineers, December 2-3, 2021 (date of event) [Patent documents]

[0005] [Patent Document 1] Patent No. 6252669 Summary of the Invention [Problem to be solved by the invention]

[0006] The compressed sensing theory used in Non-Patent Document 1 requires that the measurement data has sparsity with respect to the Fourier basis. However, the frequency spectrum may become broad (i.e., sparsity is low), making it impossible to restore the original signal with the required accuracy. Note that Non-Patent Document 1 calculates the restoration error from the power difference, but this is a retrospective evaluation.

[0007] The present invention has been made in consideration of the above problems, and has an object to provide a measurement system, a measurement and calculation device, a measurement and calculation method, and a measurement and calculation program that can increase the restoration rate of the original signal while reducing measurement data. [Means for solving the problem]

[0008] The above-mentioned object of the present invention can be achieved by the following means. The present invention relates to a sequential measurement unit that sequentially measures a measured signal (s(t)) that changes corresponding to the rotational position (rotational phase θ) or rotational speed of a rotating machine (including a rotating electric machine) at a predetermined sampling frequency or sampling angular frequency (ωs) for a first period (T1); a DFT calculation unit that performs a discrete Fourier transform on the discrete-time signal (s) measured by the sequential measurement unit and outputs a Fourier coefficient (xf); a random measurement value output unit that outputs first random measurement values ​​that are randomly measured or selected with a predetermined random matrix Φ using the measured signal (analog signal s(t)) or the discrete-time signal (s); and a first random measurement vector y1 that is a vector representation of the first random measurement values, which is calculated by multiplying the random matrix Φ by a basis vector {Ψ iLet us express the product Φψx of the n×n orthogonal basis matrix ψ with columns} and its coefficient x, and let λ be the regularization coefficient. Then, we define the coefficient x={x i a regularization coefficient setting unit that determines the regularization coefficient λ0 that is maximum within a standard deviation of cross-validation at the regularization coefficient λ with the smallest error, based on the first random measurement vector y1 and the random matrix Φ, wherein the error is a difference in power between the separation time signal and the first random measurement value, calculated using the coefficient x estimated by the estimation unit and the Fourier coefficient (xf), and the difference is within a predetermined range.

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

[0010] [Figure 1] 1 is a configuration diagram of a measurement system according to a first embodiment of the present invention. [Diagram 2] FIG. 4 is a diagram for explaining the relationship between a parameter setting period (first period) and a measurement period (second period). [Diagram 3] 10 is a diagram for explaining a difference in the number of samples of a signal under measurement depending on whether the rotation speed is high or low. FIG. [Figure 4A] FIG. 4 is a diagram showing a change in a signal under measurement over time. [Figure 4B] FIG. 2 is a diagram showing a change in the rotational phase of a rotating machine over time. [Figure 4C] 11 is a diagram showing the relationship between a signal under test and a rotation phase; FIG. [Diagram 5] 4 is a flowchart for explaining the operation of the measurement system according to the first embodiment of the present invention. [Figure 6] FIG. 13 is a diagram showing Fourier coefficients xf of a discrete-time signal successively measured in synchronization with the rotation phase. [Figure 7] FIG. 13 is a diagram showing coefficients x of an orthogonal basis matrix ψ of a signal measured by compressive sampling. [Figure 8] FIG. 1 illustrates the POA of amplitude in orders. [Figure 9] 13 is a diagram showing the online anomaly degree calculated using the Mahalanobis distance for the POA value. [Figure 10] FIG. 13 is a diagram showing a change in feature order over time when transitioning from a normal state to an abnormal state. [Figure 11] FIG. 13 is a diagram showing a time change in degree of abnormality calculated from a feature order. [Figure 12] FIG. 11 is a configuration diagram of a measurement system according to a second embodiment of the present invention. [Figure 13] 6 is a flowchart for explaining the operation of a measurement system according to a second embodiment of the present invention. [Figure 14] FIG. 11 is a configuration diagram of a measurement system according to a third embodiment of the present invention. [Figure 15] FIG. 11 is a configuration diagram of a measurement system according to a fourth embodiment of the present invention. [Figure 16] FIG. 13 is a configuration diagram of a measurement system according to a fifth embodiment of the present invention. [Figure 17] FIG. 4 is a diagram showing frequency characteristics of a general-purpose microphone and a measurement microphone. [Figure 18] FIG. 13 is a configuration diagram of a measurement system according to a sixth embodiment of the present invention. [Figure 19] FIG. 1 is a configuration diagram of a measurement system which is a first comparative example of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings. Note that each drawing is merely a schematic illustration to allow a sufficient understanding of the present invention. Therefore, the present invention is not limited to the illustrated examples. In addition, in each drawing, common components or similar components are given the same reference numerals, and duplicated explanations thereof will be omitted.

[0012] (First embodiment) FIG. 1 is a configuration diagram of a measurement system according to a first embodiment of the present invention. The measurement system 100 measures the characteristics (e.g., acoustic characteristics and vibration characteristics) of the rotating electric machine 30 using a sensor 20, and is configured by connecting a random measurement device 10, a sequential measurement device 70, and a measurement and calculation device 50 so as to be able to communicate with each other. The rotating electric machine 30 is a rotating machine in which a propeller 32 is attached to a motor 31. The propeller 32 is a normal product when it has a plurality of (e.g., seven) blades 32a, but in this embodiment, the characteristics are measured in a state in which one of the blades is missing, i.e., a missing portion 32b. The motor 31 rotates the propeller 32, and is driven by receiving power supply from the random measurement device 10, for example. The sensor 20 is, for example, a microphone, and detects the sound pressure generated by the propeller 32 via wind pressure.

[0013] The random measurement device 10 randomly samples the measured signal s(t) output by the sensor 20 in synchronization with a rotational phase θ indicating the rotational position of the rotating electric machine 30. The random measurement device 10 is configured with a random measurement unit 1 as a random measurement value output unit, and a rotational information acquisition unit 3. The rotational information acquisition unit 3 acquires the rotational phase θ of the motor 31.

[0014] The random measurement unit 1 synchronizes the measured signal s(t) with the rotation phase θ, and outputs (transmits) a signal of a first random measurement vector y1=Φs, which is a vector representation of a measurement value (first random measurement value) randomly sampled according to a random matrix Φ, or a random measurement vector y=Φs, which is a vector representation of a random measurement value, to the measurement calculation device 50. Here, the measurement period is divided into a parameter setting period (first period) in which measurement parameters (for example, a regularization coefficient λ described later) are set, and a measurement period (second period) after the parameters are set.

[0015] FIG. 2 is a diagram for explaining the relationship between a parameter setting period (first period T1) and a measurement period (second period T2) after the parameter is set. The first period T1 is from t=0 to t1, and the second period T2 is from t=t2 onwards. Note that the period from t1 to t2 is a measurement interruption period.

[0016] The random measurement vector measured in the first period T1 is the first random measurement vector y1=Φs, and the random measurement vector measured in the second period T2 (the second random measurement vector) is y=Φs. The random matrix Φ also includes a column Φ r and the matrix Φ indicating a random start rsu etc. The sequence Φ indicates random sampling. r indicates that the measured signal s(t) is measured by randomly thinning out all the time series signals (discrete time signals s) obtained at equal intervals. The matrix Φ rsu indicates that multiple measurements are taken with random measurement start times, and that a single measurement is taken at a constant angular frequency ω rsu (For example, 2πf rsu = 2π × 0.3Hz) or a constant frequency f rsu M p Points (e.g., M p= 27 points) of data are taken. As a result, the number of samples that the random measurement unit 1 takes of the signal s(t) to be measured is smaller than the number of discrete-time signals s. The random measurement unit 1 can be manufactured more inexpensively than the unit that samples and measures the signal s(t) to be measured in synchronization with the rotation phase θ and outputs a sequence of all time-series signals (discrete-time signals s).

[0017] The sequential measurement device 70 includes a sequential measurement unit 73, a DFT calculation unit 74, and a PLL 75. The PLL (Phase Locked Loop) 75 receives a signal with a rotation phase θ and generates a sampling angular frequency ω s The sequential measurement unit 73 sequentially measures the signal under test s(t) at a constant sampling angular frequency ωs while synchronizing it with the rotation phase θ, and outputs a discrete-time signal s. In particular, the matrix Φ rsu When , the sampling angular frequency ωs = Nω rsu It becomes.

[0018] A 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 randomly selects points that are not to be measured and a sampling angular frequency ωs=Nω rsu It differs from the random measurement device 10 in that

[0019] The measurement and calculation device 50 calculates the Fourier coefficient xf={xf i}, judges sparsity, and sets a parameter (regularization coefficient λ). Specifically, in a first period T1, the measurement calculation device 50 checks that n>m and n / s>n / m, where m is the number of samples after compression, n is the number of samples before compression, s is the number of non-zero q (frequency) components, and c is a constant for compressive sensing. Thereafter, the measurement calculation device 50 sets a parameter (regularization coefficient λ).

[0020] In addition, in the second period T2, the measurement and calculation device 50 restores all data (discrete-time signal s) from the small amount of random measurement values ​​(random measurement vector y=Φs) received from the random measuring device 10. Here, the discrete-time signal s is represented by a basis vector {Ψ i} is the coefficient x={x i}, it is expressed as s = ψx. Here, the basis vector {Ψ i} is, for example, a Fourier basis vector with the rotation phase θ as a variable. One period of the Fourier basis vector corresponds to one rotation of the rotating electric machine 30.

[0021] The measurement calculation device 50 is a PC (Personal Computer), and by executing a measurement 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 anomaly degree calculation unit 55, and an alarm unit 56.

[0022] The estimation unit 61 estimates the coefficient x of the n×n orthogonal basis matrix ψ by using the first random measurement vector y1=Φs received by the measurement calculation device 50 in the first period or the random measurement vector y=Φs received in the second period. Specifically, using a least absolute shrinkage and selection operator (LASSO) method, the coefficient x={x i In this case, the variable of the orthogonal basis matrix ψ is the rotation phase θ.

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[0023] Here, the norms in the formulas are defined in the following formulas (5) and (6).

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[0024] Σ|x i | is x from i=1 to N i means adding the absolute value of Σ|x i | 2 is x from i=1 to N i This means adding the square of the absolute value of . Note that (y-Φψx), obtained by subtracting the product Φψx of the random matrix Φ and the n×n orthogonal basis matrix ψ and its coefficient x from the random measurement vector y, represents an error.

[0025] The regularization coefficient setting unit 62 sets a parameter (regularization coefficient λ) in the first period T1. Specifically, the regularization coefficient setting unit 62 sets the value of the regularization coefficient λ to λ=λ0, which is the maximum value within the standard deviation of the cross-validation at λ with the smallest error.

[0026] In the first period T1, the restoration error calculation unit 54 calculates the Fourier coefficient xf={xf i} and coefficient x={x i} to obtain the power difference between the discrete-time signal s and the first random measurement value (the vector representation of which is the first random measurement vector y1). Furthermore, the restoration error calculation unit 54 divides the power difference by the square sum of the coefficient x to calculate the restoration error r (equation (7)). The restoration error calculation unit 54 checks whether the restoration error r falls within a predetermined range (for example, 0.01%, 0.1%, 1%, 10%, 20%), and corrects the regularization coefficient λ=λ0 if it does not fall within the predetermined range.

[0027]

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[0028] In the second period T2, the restoration unit 63 calculates the n×n orthogonal basis matrix ψ and the coefficient x={x i} to restore the discrete-time signal s=ψx. In other words, the restoration unit 63 restores the entire discrete-time signal s using the random measurement vector y=Φs that is randomly sampled.

[0029] The abnormality degree calculation unit 55 calculates the abnormality degree in the second period by using, for example, the Mahalanobis distance (online). {x 1,1 ,x 1,2 ,···,x 1,n},····,{x p,1 ,x p,2 ,···,x p,n} is set as the approximate normal value, and new p input values ​​are {x 1,n+1,····, x p,n+1} The Mahalanobis distance D n+1 is shown in equation (8).

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[0030] Here, Dd n+1 is the difference vector shown in equation (9).

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[0031]

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[0032]

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[0033] Initial values ​​Ax1, V1 -1 After preparing the above, the degree of anomaly can be calculated by sequentially calculating equations (8) through (11) starting from n=1.

[0034] When the abnormality degree calculation unit 55 detects an abnormality, that is, when the Mahalanobis distance Dn+1 When the degree of abnormality obtained by using exceeds the threshold value α, the user is notified. The threshold value α is determined according to the upper probability u. Here, the upper probability u refers to the probability that a random variable becomes larger than a certain value. For example, when the upper probability u=0.05, the threshold value α=3.75, and when the upper probability u=0.01, the threshold value α=4.30 is representative.

[0035] FIG. 3 is a diagram for explaining the difference in the number of samples of the measured signal s(t) depending on the rotation speed. The horizontal axis is time t, and the vertical axis in the diagram below is the measured signal s(t). The measured signal s(t) is a sine wave signal, with the first period from time 0 to t1 being a high rotation speed, and the second period from time t1 to t2 being a low rotation speed. In the diagram below, the points where the measured signal s(t) is sampled in synchronization with the rotation phase θ are indicated by white circles (○). For example, in the lower diagram of Figure 2, white circles (○) are placed every 40° of the rotation phase θ. In addition, vertical lines of the same timing are drawn on the horizontal lines in the diagram above. Whether in the high rotation speed region A or the low rotation speed region B, the number of samples per period is the same.

[0036] In addition, one rotation is one cycle, and the phenomenon that occurs once is defined as the first rotation component, and n times that is defined as the nth rotation component. An analysis in which the X-axis represents the order and the Y-axis represents the magnitude of the vibration noise of the order component is called a "rotation order ratio analysis."

[0037] Fig. 4A is a diagram showing a change over time in the signal under test. The horizontal axis represents time t, and the vertical axis represents the signal under test s(t). Fig. 4B is a diagram showing a change over time in the rotation phase of the rotating machine (rotating electric machine 30). The horizontal axis is time t, and the vertical axis is rotation phase θ(t). Here, the measured signal s(t) is assumed to be a sine wave signal whose frequency gradually increases. Black circles (●) are marked at multiple measurement points a, b, c, and d of the measured signal s(t) and the rotation phase θ(t).

[0038] In Figure 4B, at time t = 0, the rotation phase θ(0) = 0, and the rotation phase θ(t) monotonically increases with time (measurement points a → b → c → d). For example, at point b (Figure 4A), since it is just before the third period, the rotation phase is less than (360 × 4)°. At point c (Figure 4A), since it is just before the fifth period, the rotation phase is more than (360 × 4)°. At point d (Figure 4A), it is six periods later, and the rotation phase is between (360 × 4)° and (360 × 8)°.

[0039] FIG. 4C is a diagram showing the relationship between the signal under measurement and the rotation phase. The horizontal axis represents the rotation phase θ, and the vertical axis represents the signal under test s(θ). Between cd, the time T3 (FIG. 4A) is short, but the rotational phase width Θ1 is expressed as long. In other words, as shown in FIG. 4C, if the rotational phase θ is a variable, the measured signal s(θ) can be evaluated as a sine wave even if the rotational speed of the rotating electric machine 30 changes.

[0040] 5 is a flowchart for explaining the operation of the measurement system according to the first embodiment of the present invention. This flow is started when a new measurement target is measured or when the measurement target is changed. As a result, the measurement calculation device 50 predetermines a parameter (e.g., a regularization coefficient λ0) in the first period T1, and starts measurement using the regularization coefficient λ0 in the second period T2.

[0041] In a first period T1, the random measurement device 10 randomly acquires a measurement value of a measured signal s(t) from the sensor 20 (step S1). At this time, the random measurement device 10 receives a signal of a rotation phase θ(t) from the rotating electric machine 30. As a result, in the random measurement device 10, the random measurement unit 1 (FIG. 1) generates a random measurement vector y=Φs.

[0042] The random measuring device 10 also transmits the received signal of the rotation phase θ(t) to the PLL 75 of the sequential measuring device 70. As a result, the PLL 75 generates a signal with a sampling angular frequency ωs, which is a higher angular frequency than the rotation angular velocity ω=dθ / dt of the rotating electric machine 30. Then, the sequential measuring unit 73 (FIG. 1) sequentially acquires the measured signal s(t) at a constant sampling angular frequency ωs (step S2). The sequential measuring unit 73 (FIG. 1) generates a discrete-time signal s, and the DFT calculation unit 74 uses the discrete-time signal s to calculate the Fourier coefficients xf={xf i} (step S3). The variable of the orthogonal basis matrix ψ at this time is time t. After the process of step S3, the sequential measuring device 70 transmits the calculated Fourier coefficients xf to the measurement calculation device 50 (step S4).

[0043] After the process of step S1, the random measuring device 10 transmits a random measurement vector (first random measurement vector y1) to the measurement calculation device 50 (step S5), and continues randomly acquiring the measurement value of the measured signal s(t) (step S6) and transmitting it to the measurement calculation device 50 (step S7). After the process of step S5, the measurement calculation device 50 receives the random measurement vector (first random measurement vector y1) (step S8), and the regularization coefficient setting unit 62 determines the regularization coefficient λ0 (step S9). At this time, the estimation unit 61 uses the LASSO technique to set the variables of the n×n orthogonal basis matrix ψ to the rotation phase θ, and the coefficient x={x i In addition, the regularization coefficient setting unit 62 determines the regularization coefficient λ0 so that it becomes the maximum value within the standard deviation of the cross validation at λ with the smallest error (step S9).

[0044] After the process of step S9, the measurement calculation device 50 sequentially receives the Fourier coefficients xf from the measuring device 70 (step S10). After the process of step S10, in the measurement calculation device 50, the restoration error calculation unit 54 calculates the restoration error r and determines whether the calculated restoration error r is within a predetermined range (step S11). If the restoration error r is outside the predetermined range (within the predetermined range at step S11), the measurement calculation device 50 returns the process to S9 and resets the regularization coefficient λ0. On the other hand, if the restoration error r is within the predetermined range (within the predetermined range at step S11), the measurement calculation device 50 receives the random measurement vector y from the random measuring device 10 (step S12) and calculates the coefficient x={x i} is estimated (step S13). At this time, the variable of the orthogonal basis matrix ψ is the rotation phase θ.

[0045] After the process of step S13, the measurement calculation device 50 judges whether the degree of abnormality calculated by the abnormality degree calculation unit 55 exceeds the threshold value α (step S14). If the degree of abnormality does not exceed the threshold value α (below the threshold value in step S14), the measurement calculation device 50 returns the process to step S12 and continues receiving the random measurement vector y. On the other hand, if the degree of abnormality exceeds the threshold value α (above the threshold value in step S14), the notification unit 56 of the measurement calculation device 50 notifies the user that the measured signal s(t) is abnormal (step S15). Note that in the measurement calculation device 50, the restoration unit 63 restores the coefficient x={x i} to reconstruct the discrete-time signal s=ψx.

[0046] Figure 6 shows the Fourier coefficients xf = {xf i 5 is a diagram showing the results of calculations performed by the DFT calculation unit 74 (FIG. 1) in the first period T1 (FIG. 2). The horizontal axis represents the order, and the vertical axis represents the Fourier coefficient xf at each order. The 7th order spectrum is higher than the 1st order spectrum.

[0047] Figure 7 shows the coefficients x={x i7 is a diagram showing an estimation result of the coefficient x estimated by the estimation unit 61 in the first period T1. The horizontal axis represents the order ratio, and the vertical axis represents the coefficient x for each order. As in Figure 6, the 7th order spectrum is higher than the 1st order spectrum. Note that the Fourier coefficient xf = {xf i}(Figure 6) and coefficient x={x i}(Figure 7), the difference between them is (xf-x)={xf i}-{x i} occurs. Here, the difference (xf-x) = {xf i}-{x i In order to calculate {}, it is necessary to subtract between orders or between frequencies. In other words, it is necessary to subtract coefficients by making the variables of the orthogonal basis matrix ψ be times t or rotation phases θ.

[0048] FIG. 8 is a diagram showing the POA of the amplitude in the order. The horizontal axis is the characteristic order (feature order). The solid line is the POA calculated using the coefficient x calculated by the estimation unit 61 in the first period T1. The dashed line is the POA calculated using the Fourier coefficient xf calculated by the DFT calculation unit 74 in the first period T1. Note that POA (partial overall) refers to the sum (product sum) of power within a predetermined spectrum interval. Note that "overall" refers to the sum (product sum) of power of all frequencies. The POA has a peak at the seventh order. In addition, there is a certain difference (about 0.005) between the POA using the coefficient x and the POA using the Fourier coefficient Xf.

[0049] FIG. 9 is a graph showing the online anomaly degree calculated using the Mahalanobis distance for the POA value. For the first to seventh components, the graph shows the "normal abnormality degree" when the component is normal, the "half-chipped abnormality degree" when the chipped portion 32b is half-chipped, and the "total-chipped abnormality degree" when the chipped portion 32b is completely chipped. Note that the abnormality degree is set to p=1.

[0050] For the seventh-order component, the normal abnormality degree, the half-missing abnormality degree, and the total missing abnormality degree are all at the same level. On the other hand, for the first to third-order components, the half-missing abnormality degree and the total missing abnormality degree are higher than the normal abnormality degree. In particular, the total missing abnormality degree of the third-order component is twice as high as the half-missing abnormality degree.

[0051] 10 is a diagram showing the change in the feature order over time when transitioning from a normal state to an abnormal state. The solid line is the first-order component, the dotted line is the second-order component, and the dashed line is the seventh-order component. In an abnormal state, the first-order component increases significantly and the second-order component increases slightly.

[0052] FIG. 11 is a diagram showing the change over time in the degree of abnormality calculated from the feature order. The degree of abnormality (solid line) was calculated using the first to seventh order components of the amplitude (Fig. 10) with p = 7. The dashed line indicates the judgment period, during which judgment is made after a predetermined time (e.g., t = 1750 hours) has elapsed. The horizontal axis indicates time t. Even if the state is normal at first, after a long time has elapsed, abnormal and normal states will be repeated. The notification unit 56 (Fig. 1) issues a notification when the degree of abnormality exceeds a threshold value α (e.g., α = 3.75).

[0053] Second embodiment In the above embodiment, during the second period T2, the random measuring device 10 (FIG. 1) randomly acquired the measured signal s(t) by synchronizing it with the rotation phase θ, but the measured signal s(t) can also be randomly acquired at a predetermined sampling frequency fs or sampling angular frequency ωs.

[0054] FIG. 12 is a configuration diagram of a measurement system according to a second embodiment of the present invention. The measurement system 101 includes a random measurement device 11 , a sequential measurement device 71 , and a measurement and calculation device 51 . The random measurement device 11 differs from the random measurement device 10 of the embodiment in that it does not have a rotation information acquisition unit 3. That is, the random measurement unit 1 drives the measured signal s(t) at a predetermined sampling frequency fs or sampling angular frequency ωs without synchronizing with the rotation phase θ (FIG. 1), measures it randomly, and outputs a random measurement vector y=Φs. 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. 1) of the embodiment in that it has a sampling frequency generator 76 instead of a PLL 75 (FIG. 1). That is, the sequential measurement unit 73 sequentially measures the measured signal s(t) at the sampling frequency fs or sampling angular frequency ωs generated by the sampling frequency generator 76. Note that the random measurement unit 1 and the sequential measurement unit 73 are driven at a predetermined sampling frequency fs or sampling angular frequency ωs, but the sampling frequency fs and the sampling angular frequency ωs may be different, and they do not need to be synchronized.

[0055] Like the measurement calculation device 50 of the first embodiment, the measurement calculation device 51 includes a restoration error calculation unit 54, an abnormality degree calculation unit 55, a notification unit 56, an estimation unit 61, a regularization coefficient setting unit 62, and a restoration unit 63. However, the measurement calculation device 51 differs from the measurement calculation device 50 of the above embodiment in that it includes a random selection unit 57 and a switch 58.

[0056] The random selection unit 57 randomly selects a discrete-time signal s sequentially output by the sequential measurement unit 73 in the first period T1 according to the random matrix Φ. In other words, the random selection unit 57 also functions as a random measurement value output unit, and outputs a first random measurement vector y1=Φs that is a vector representation of the random measurement value. The switch 58 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 57, 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. The estimation unit 61 selects the Fourier basis vector {Ψ i The variable of { is time t.} This differs from the first embodiment in which the rotation phase θ is a variable.

[0057] In the first period T1, the estimation unit 61 inputs the first random measurement vector y1=Φs output by the random selection unit 57, as in the first embodiment, 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 the cross-validation at λ with the smallest error. In addition, the restoration error calculation unit 54 resets the regularization coefficient λ0 when the restoration error r is not within a predetermined range. Note that the random measurement unit 1 also outputs the first random measurement vector y1=Φs, but is blocked by the switch 58.

[0058] In the second period T2, the estimation unit 61 uses the regularization coefficient λ0 set in the first period T1 to input the random measurement vector y=Φs output by the random measurement unit 1 and estimates the coefficient x of the n×n orthogonal basis matrix ψ. Furthermore, as in the first embodiment, the restoration unit 63 restores the discrete-time signal s.

[0059] FIG. 13 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, in the sequential measurement device 71, the sequential measurement unit 73 sequentially acquires the measured signal s(t) at a predetermined sampling frequency fs or sampling angular frequency ωs (step S21). After the process of step S21, the sequential measurement device 71 transmits the discrete-time signal s to the measurement and calculation device 51 (step S22), and the measurement and calculation device 51 receives the discrete-time signal s (step S23).

[0060] In the measurement calculation device 51, the random selection unit 57 randomly selects the discrete-time signal s according to the random matrix Φ (step S24), and the regularization coefficient setting unit 62 uses the first random measurement vector y1=Φs to determine the regularization coefficient λ0 (step S25). Meanwhile, in the sequential measurement device 71, the DFT calculation unit 74 calculates the Fourier coefficient xf (step S26) and transmits the Fourier coefficient xf to the measurement calculation device 51 (step S27). In the measurement calculation device 51, the Fourier coefficient xf is received (step S28), 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 S29). When the restoration error r is outside the predetermined range (outside the predetermined range in step S29), the measurement calculation device 51 returns the process to S25 and causes the regularization coefficient setting unit 62 to reset the regularization coefficient λ0. On the other hand, when the recovery error r falls within the predetermined range (within the predetermined range in step S29), the measurement system 101 transitions to the second period T2 (FIG. 2).

[0061] In the second period T2, in the random measurement device 11, the random measurement unit 1 randomly acquires a measurement value of the signal s(t) under measurement (step S30) and transmits a random measurement vector y=Φs to the measurement and calculation device 51 (step S31). In the measurement and calculation device 51, the random measurement vector y=Φs is received (step S32), and the estimation unit 61 estimates the coefficient x={x i} is estimated (step S33).

[0062] After the process of step S33, in the measurement calculation device 51, the abnormality degree calculation unit 55 calculates the abnormality degree and determines whether or not the abnormality degree exceeds the threshold value α (step S34). If the abnormality degree is equal to or less than the threshold value α (below threshold in step S34), the measurement calculation device 51 returns the process to step S32 and continues receiving the random measurement vector y=Φs. On the other hand, if the abnormality degree exceeds the threshold value α (above threshold in step S34), the measurement calculation device 51 causes the notification unit 56 to issue a notification (step S35).

[0063] Third embodiment In the second embodiment, in the first period T1, the random selection unit 57 randomly selects the discrete-time signal s acquired at the sampling frequency fs or the sampling angular frequency ωs, creates the first random measurement vector y1=Φs, and in the second period T2, the random measurement unit 1 outputs the random measurement vector y=Φs. However, it is also possible to cause the random measurement unit 1 to output the first random measurement vector y1=Φs in the first period.

[0064] FIG. 14 is a configuration diagram of a measurement system according to the third embodiment of the present invention. The measurement system 102 comprises a random measurement device 11, a sequential measurement device 72, and a measurement and calculation device 50. The random measurement device 11 has the same configuration as that of the second embodiment, and the measurement and calculation device 50 has the same configuration as that of the first embodiment, but the Fourier basis vectors {Ψ i} has time t as a variable, which differs from the first embodiment having the rotation phase θ as a variable.

[0065] The sequential measurement device 72 has a sequential measurement unit 73, a DFT calculation unit 74, and a sampling frequency generator 76, similar to the second embodiment, but differs in that the discrete-time signal s is not output from the sequential measurement unit 73 to the measurement calculation device 50.

[0066] In the first period T1, the random measurement unit 1 of the random measurement device 11 randomly acquires the measurement value of the signal under test s(t) and outputs a first random measurement vector y1=Φs to the estimation unit 61 and regularization coefficient setting unit 62 of the measurement calculation device 50. In addition, the DFT calculation unit 74 of the sequential measurement device 72 outputs the Fourier coefficient xf={xf i}. From these, the regularization coefficient λ=λ0 is determined so that the recovery error r falls within a predetermined range.

[0067] In the second period T2, the random measurement unit 1 of the random measurement device 11 randomly acquires the measurement value of the measured signal s(t) and outputs the random measurement vector y=Φs to the estimation unit 61 and regularization coefficient setting unit 62 of the measurement calculation device 50. As a result, the estimation unit 61 estimates the coefficient x, and the restoration unit 63 restores the discrete-time signal s=ψx. In addition, the anomaly degree calculation unit 55 sequentially calculates the anomaly degree, and when the anomaly degree exceeds the threshold value α, the notification unit 56 issues a notification.

[0068] (Fourth embodiment) In the measurement system of each of the above embodiments, during the second period T2, the coefficient x is sequentially estimated using the random measurement vector y=Φs sequentially received by the measurement calculation device 50, 51. However, the random measurement vector y=Φs sequentially received by the measurement calculation device can be stored in a memory unit, and batch processing can be performed using the random measurement vector y=Φs stored in the memory unit.

[0069] FIG. 15 is a configuration diagram of a measurement system according to the fourth embodiment of the present invention. The measurement system 103 includes a random measuring device 11, a measurement and calculation device 52, and a sequential measuring device 72. The random measuring device 11 and the measurement and calculation device 52 have the same configuration as those in the third embodiment. The measurement and calculation device 52 differs from the measurement and calculation device 50 in the third embodiment in that it includes a storage unit 59.

[0070] The storage unit 59 stores the random measurement vector y=Φs for the second period T2. As a result, the measurement calculation device 52 determines the regularization coefficient λ=λ0 using the received first random measurement vector y1=Φs in the first period T1, and the random measurement vector y=Φs is stored in the storage unit 59 in the second period T2. After that, the restoration unit 63 restores the discrete-time signal s=ψx in batch processing.

[0071] Fifth embodiment In each of the above-described embodiments (particularly, the fourth embodiment), the type of microphone was not selected for the sensor 20. In this embodiment, the sensor used in the sequential measurement unit 73 (FIG. 16) is a measurement microphone, and the sensor (general-purpose sensor 21) used in the random measurement unit 1 is a general-purpose microphone made of simple MEMS (Micro Electro Mechanical Systems).

[0072] FIG. 16 is a configuration diagram of a measurement system according to the fifth embodiment of the present invention. The measurement system 104 includes a random measurement device 12, a measurement calculation device 53, and a sequential measurement device 72, similar to the measurement system 103 (FIG. 15) of the fourth embodiment. The random measurement device 12 differs from the random measurement device 11 (FIG. 15) in that the random measurement device 12 further includes a switch 2 that switches between the general-purpose sensor 21 and the measurement sensor 22. The measurement calculation device 53 differs from the measurement calculation device 52 (FIG. 15) in that the measurement calculation device 53 further includes a frequency correction unit 66 and a switch 67. The sequential measurement device 72 also connects the measurement sensor 22 instead of the sensor 20 (FIG. 15). The frequency correction unit 66 is connected to the storage unit 59 and corrects the frequency characteristics of the data (random measurement vector y=Φs) of the general-purpose sensor 21 stored in the storage unit 59. As a result, the general-purpose sensor 21 and the frequency correction unit 66 become equivalent to the measurement sensor 22 as a whole.

[0073] The switch 2, 67 is a two-contact switch that connects either the terminal a or b to the terminal c. The switch 2, 67 is connected to the terminal b in the first period T1 (FIG. 2), and is connected to the terminal a in the second period T2 (FIG. 2). That is, the switch 2 connects the measurement sensor 22 to the random measurement unit 1 in the first period T1, and connects the general-purpose sensor 21 to the random measurement unit 1 in the second period T2. The switch 67 connects the storage unit 59 to the estimation unit 61 and the regularization coefficient setting unit 62 in the first period T1, and connects the frequency correction unit to the estimation unit 61 and the regularization coefficient setting unit 62 in the second period T2.

[0074] The general-purpose sensor 21 is, for example, a MEMS sensor, specifically, a general-purpose microphone made of MEMS. The measurement sensor 22 is a measurement microphone, and has better frequency sensitivity than a general-purpose microphone.

[0075] FIG. 17 is a diagram showing frequency characteristics of a general-purpose microphone and a measurement microphone. The horizontal axis is frequency [Hz] and the vertical axis is decibels. The solid line shows the characteristics of the measurement microphone, and the dashed line shows the characteristics of a general-purpose MEMS microphone. The solid and dashed lines are 0 decibels at a reference frequency of 1 kHz. The measurement microphone maintains a flat frequency characteristic from about 20 Hz to about 20 kHz. In contrast, the output of the general-purpose MEMS microphone drops at low frequencies from about 20 Hz to 200 Hz.

[0076] 16, the general-purpose sensor 21 is connected to the terminal b of the switch 2, and the measurement sensor 22 is connected to the terminal a. The measurement sensor 22 is also connected to the sequential measurement unit 73. In the measurement calculation device 53, the input terminal of the frequency correction unit 66 and the terminal a of the switch 67 are connected to the output terminal of the storage unit 59. The output terminal of the frequency correction unit 66 is connected to the terminal b of the switch 67, and the terminal c of the switch 67 is connected to the regularization coefficient setting unit 62 and the estimation unit 61.

[0077] With these configurations, in the first period T1 (FIG. 2), the random measurement unit 1 and the sequential measurement unit 73 measure the sound pressure using the measurement sensor 22. In the measurement and calculation device 53, the memory unit 59 stores the random measurement vector y1=Φs in the first period T1. The regularization coefficient setting unit 62 sets the regularization coefficient λ=λ0 so that the restoration error r falls within a predetermined range. In addition, in the second period T2 (FIG. 2), the random measurement unit 1 measures the sound pressure using the general-purpose sensor 21. In the measurement and calculation device 53, the memory unit 59 stores the random measurement vector y=Φs in the second period T2, and the frequency correction unit 66 corrects the frequency characteristics. The estimation unit 61 uses the corrected random measurement vector y=Φs to estimate the coefficient x with the set regularization coefficient λ0. Furthermore, the restoration unit 63 restores the discrete-time signal s.

[0078] Sixth embodiment A microphone was not selected as the sensor 20 used in the first embodiment. In this embodiment, a sensor (general-purpose sensor 21) used in the random measurement unit 1 is a general-purpose microphone made of MEMS, and a sensor used in the sequential measurement unit 73 (FIG. 15) is a measurement microphone.

[0079] FIG. 18 is a configuration diagram of a measurement system according to the sixth embodiment of the present invention. The measurement system 105 includes a random measurement device 13, a measurement calculation device 80, and a sequential measurement device 70, similar to the measurement system 100 (FIG. 1) of the first embodiment. The random measurement device 13 differs from the random measurement device 10 (FIG. 1) in that it further includes a switch 2 that switches between the general-purpose sensor 21 and the measurement sensor 22. The measurement calculation device 80 differs from the measurement calculation device 50 (FIG. 1) in that it further includes a frequency correction unit 66 and a switch 67. In addition, the sequential measurement device 70 connects the measurement sensor 22 instead of the sensor 20 (FIG. 1).

[0080] With these configurations, in the first period T1 (FIG. 2), the random measurement unit 1 and the sequential measurement unit 73 measure the sound pressure using the measurement sensor 22. In the measurement and calculation device 80, the regularization coefficient setting unit 62 sets the regularization coefficient λ=λ0 using the random measurement vector y1=Φs in the first period T1 so that the restoration error r falls within a predetermined range. In addition, in the second period T2 (FIG. 2), the random measurement unit 1 measures the sound pressure using the general-purpose sensor 21. In the measurement and calculation device 80, the frequency correction unit 66 corrects the frequency characteristics for the random measurement vector y=Φs in the second period T2. The estimation unit 61 uses the corrected random measurement vector y=Φs to estimate the coefficient x with the set regularization coefficient λ0. Furthermore, the restoration unit 63 restores the discrete-time signal s.

[0081] FIG. 19 is a configuration diagram of a measurement system which is a first comparative example of the present invention. The measurement system 106 is configured by connecting the measuring device 14 and a measurement calculation device 81 so as to be able to communicate with each other. The measuring device 14 includes a synchronous measurement unit 79 that sequentially measures the measured signal s(t) of the sensor 20 in synchronization with the rotation phase θ and outputs a discrete-time signal s. In other words, the measuring device 14 differs from the random measuring devices 10 (FIG. 1) to 13 (FIG. 18) of the above-described embodiments in that it does not randomly sample.

[0082] The measurement calculation device 81 includes a receiving unit 69, an x ​​calculation unit 64, and a restoration unit 65. The receiving unit 69 receives a discrete-time signal s from the measuring device 14. The x calculation unit 64 calculates a coefficient (Fourier coefficient xf) of a Fourier basis vector ψf. Here, the variable of the Fourier basis vector ψf is time t. That is, the x calculation 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.

[0083] In addition, since the measuring device 14 sequentially acquires the measured signal s(t) in synchronization with the rotation phase θ, the measurement calculation device 81 can perform a discrete Fourier transform using the rotation phase θ as a variable, but since the measured signal s(t) is randomly sampled in each of the above embodiments, a discrete Fourier transform cannot be performed. However, in the measurement calculation device 50 of the above embodiments, the coefficient x of the n×n orthogonal basis matrix ψ is made sparse by solving L1 regularization using LASSO (Least Absolute Shrinkage and Selection Operator).

[0084] (Modification) The present invention is not limited to the above-described embodiments, and modifications can be made without departing from the spirit of the present invention. For example, the following modifications are possible. (1) In the measurement systems 100 (FIG. 1), 101 (FIG. 12), 102 (FIG. 14), and 103 (FIG. 15) of the above embodiments, the random measuring device 10 and the measurement and calculation device 50 are connected to each other so as to be capable of communicating with each other, but they may also be configured as an integrated unit.

[0085] (2) In the random measuring device 10 (FIG. 1) of the first embodiment, the random measuring device 10 is synchronized with the rotation phase θ indicating the rotation position of the rotating electric machine 30, but even in the case of the rotation speed, the rotation position can be calculated by performing unwrapping and integration processing. That is, the rotation information acquisition unit 3 acquires information on the rotation position or rotation speed of the rotating electric machine 30, and the random measuring device 10 performs random sampling in synchronization with the information on the rotation position or rotation speed of the rotating electric machine 30.

[0086] (3) In each of the above embodiments, the restoration error calculation unit 54 calculates the coefficient x={x i} and the Fourier coefficient xf={xf i}, and the square sum of the difference is used to calculate the power difference between the discrete-time signal s and the first random measurement value. i} and calculate the first power of the sum of squares of the Fourier coefficients xf={xf i} and calculating the difference between the first power and the second power, the power difference between the discrete-time signal s and the first random measurement vector y1 can be calculated. This eliminates the need to subtract between orders or frequencies. In other words, it is not necessary to set the variables of the orthogonal basis matrix ψ to times t or rotation phases θ and subtract coefficients. In other words, in the first embodiment (FIG. 1), the sampling frequency generator 76 (FIG. 12) can be used instead of the PLL 75.

[0087] (4) In the fifth and sixth embodiments, the general-purpose sensor 21 and the measurement sensor 22 are used, but only the general-purpose sensor 21 may be used. In this case, in the fifth embodiment (FIG. 16), it is necessary to provide a frequency correction unit 66 not only at the output of the storage unit 59 but also between the DFT calculation unit 74 and the restoration error calculation unit 54. In the sixth embodiment (FIG. 18), it is also necessary to provide a frequency correction unit 66 not only between the random measurement unit 1 and the regularization coefficient setting unit 62 and the estimation unit 61 but also between the DFT calculation unit 74 and the restoration error calculation unit 54.

[0088] (5) In each of the above embodiments, the sound pressure of a rotating electric machine 30 having a propeller 32 attached to a motor 31 is measured, but the vibration and sound pressure of a rotating machine (including a rotating electric machine) such as a bearing can also be measured. [Explanation of symbols]

[0089] 1 Random measurement section (measurement section) 3. Rotation information acquisition section 10,11,12,13 Random measuring equipment 14 Measuring equipment 20 Sensors 21 General-purpose sensors 22 Measurement Sensors 30 Rotating Electric Machines (Rotating Machines) 50, 51, 52, 53, 80, 81 Measurement and calculation device 54 Restoration error calculation section 55 Abnormality calculation section 56 Notification Department 57 Random Selection Section 59 Memory section 61 Estimation part 62 Regularization coefficient setting unit 66 Frequency correction section 70,71,72 Sequential measuring equipment 73 Sequential measurement section 74 DFT calculation section 100,101,102,103,104,105,106 Measurement system s(t),s(θ) Signal under test s discrete time signal θ Rotational phase (rotational position) y1 First random measurement vector y random measurement vector (second random measurement vector) Φ Random matrix λ,λ0 Regularization coefficient x coefficient ψ orthogonal basis matrix r Reconstruction error

Claims

1. a sequential measurement unit that sequentially measures a measurement signal that changes in response to a rotational position or a rotational speed of the rotating machine at a predetermined 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 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 signal under test or the discrete-time signal; 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 (3) defined by the formulas (1) and (2) 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 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: [0010] [0025] [0030]

2. The power difference is the sum of the squares of the differences between the coefficient x and the Fourier coefficients 2. The measurement system according to claim 1 .

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

2. The measurement system according to claim 1 .

4. a random measurement unit configured to randomly measure the signal under test during a second period following the first period based on the random matrix Φ; The estimation unit uses the determined regularization coefficient λ0 to express the second random measurement vector y randomly measured by the random measurement unit as a product Φψx of the random matrix Φ and the n×n orthogonal basis matrix ψ and its coefficient x, and calculates a coefficient x={x ｉ } is estimated.

2. The measurement system according to claim 1 . [0045]

5. the signal to be measured during the first period is a signal to be measured by a measurement sensor, the measured signal randomly measured by the random measurement unit during the second period is measured by a general-purpose sensor having a frequency characteristic worse than that of the measurement sensor, A frequency correction unit corrects the second random measurement vector y output by the random measurement unit using a frequency characteristic of the general-purpose sensor, The estimation unit, during the second period, uses the output data of the frequency correction unit to calculate a coefficient x={x ｉ } is estimated.

5. The measurement system according to claim 4.

6. A storage unit that stores the second random measurement vector y output by the random measurement unit during the second period, The estimation unit estimates coefficients x={x ｉ } is estimated.

5. The measurement system according to claim 4.

7. an abnormality degree calculation unit that calculates an abnormality degree for the coefficient x during the second period; a notification unit that notifies when the abnormality degree calculation unit detects an abnormality; The measurement system of claim 4 further comprising:

8. The random matrix is ​​a matrix indicating that the signal under test is randomly decimated.

2. The measurement system according to claim 1 .

9. The random matrix Φ is a matrix indicating that the measurement start time is randomized.

2. The measurement system according to claim 1 .

10. The basis vectors {Ψ ｉ } is a Fourier basis vector with time as a variable, The coefficient x is a Fourier coefficient.

2. The measurement system according to claim 1 .

11. the random measurement value output unit outputs a value of the measured signal synchronized with the rotational position or the rotational speed, the random measurement unit measures the signal under measurement in synchronization with the rotational position or the rotational speed, The basis vectors {Ψ ｉ } is a Fourier basis vector with the rotational position as a variable, The coefficient x is a Fourier coefficient.

5. The measurement system according to claim 4.

12. A first random measurement vector y1 is obtained by vector-representing a first random measurement value measured randomly with a predetermined random matrix Φ during a first period using a measured signal that changes in response to the rotational position or rotational speed of a rotating machine, and the first random measurement vector y1 is obtained by vector-representing a first random measurement value measured randomly with a predetermined random matrix Φ during a first period using the random matrix Φ and a basis vector {Ψ ｉ The orthogonal basis matrix ψ of n×n, whose columns are {x}, is expressed as the product Φψx of its coefficient x, and the regularization coefficient is λ0. Then, the coefficient x of the orthogonal basis matrix ψ is calculated so that the formula (7) defined by formulas (5) and (6) is minimized. ｉ }; and A regularization coefficient setting unit that determines the regularization coefficient λ 0 based on the first random measurement vector y 1 and the random matrix Φ so as to be a maximum value within a standard deviation of cross-validation at the regularization coefficient λ with the smallest error; the error is a difference in power between the discrete-time signal and the first random measurement value, the difference being calculated using a coefficient x estimated by the estimation unit and a Fourier coefficient obtained by performing a discrete Fourier transform on a discrete-time signal obtained by sequentially measuring the signal under measurement at a predetermined sampling frequency or sampling angular frequency; The difference is within a predetermined range A measurement and calculation device comprising: [0050] [006] [0070]

13. A first random measurement vector y1 is obtained by vector-representing a first random measurement value measured randomly with a predetermined random matrix Φ during a first period using a measured signal that changes in response to the rotational position or rotational speed of a rotating machine, and the first random measurement vector y1 is obtained by vector-representing a first random measurement value measured randomly with a predetermined random matrix Φ during a first period using the random matrix Φ and a 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 expressed as x = {x ｉ }; and A regularization coefficient setting step of determining the regularization coefficient λ 0 so as to be a maximum value within a standard deviation of cross-validation at the regularization coefficient λ with the smallest error based on the first random measurement vector y 1 and the random matrix Φ; the error is a difference in power between the discrete-time signal and the first random measurement value, the difference being calculated using a coefficient x estimated in the estimation step and a Fourier coefficient obtained by performing a discrete Fourier transform on a discrete-time signal obtained by sequentially measuring the signal under test at a predetermined sampling frequency or sampling angular frequency; The difference is within a predetermined range A measurement and calculation method comprising: [0080] [0090] [0010]

14. A first random measurement vector y1 is obtained by expressing a vector of a first random measurement value, which is measured randomly in a first period with a predetermined random matrix Φ using a measured signal that changes in response to the rotational position or rotational speed of a rotating machine, by using the random matrix Φ and a 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 product Φψx by the coefficient x of the orthogonal basis matrix ψ so that the formula (13) defined by the formulas (11) and (12) is minimized. ｉ }; and A regularization coefficient setting step of determining the regularization coefficient λ 0 based on the first random measurement vector y 1 and the random matrix Φ so as to be a maximum value within a standard deviation of cross-validation at the regularization coefficient λ with the smallest error; the error is a difference in power between the discrete-time signal and the first random measurement value, the difference being calculated using a coefficient x estimated in the estimation step and a Fourier coefficient obtained by performing a discrete Fourier transform on a discrete-time signal obtained by sequentially measuring the signal under test at a predetermined sampling frequency or sampling angular frequency; The difference is within a predetermined range A measurement calculation program comprising: ##EQU00011## ##EQU00012## ##EQU00013##

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