JPH11173908A - Method and apparatus for processing signal waveform - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make signal waveform detailedly analyzable with a simple constitution by calculating the frequency and amplitude of a signal waveform from a complex signal having a sampled signal series as a real number part (imaginary number part) and a Hilbert transformation pair of the series as an imaginary number part (real number part if the series is made the imaginary number part). SOLUTION: A signal waveform detected by a sensor 10 is sampled at a constant time interval by a sampling device 12, converted to a time series data and stored in a memory 14. A first operating device 16 calculates a discrete Hilbert transformation pair of the time series data with the use of a predetermined method, thereby obtaining a complex signal which has, for example, the time series data set as a real number part and the discrete Hilbert transformation pair as an imaginary number part. A second operating device 18 calculates a frequency from a deflection angle of the complex signal according to a predetermined expression. A third operating device 20 calculates an amplitude based on an absolute value of the complex signal according to a predetermined expression. In this constitution, the frequency and amplitude of measured data can be calculated highly accurately.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and apparatus for processing a signal waveform, and more particularly to a technique for observing the frequency of a signal waveform such as vibration and sound of mechanical equipment typified by a rotating machine and the like, and its components. About.

[0002]

2. Description of the Related Art Conventionally, a serious accident of machinery and equipment has been performed by immediately judging a sign of abnormality of the machinery and equipment during operation, stopping the apparatus and performing maintenance such as repair or replacement of parts before the abnormality spreads. In order to prevent damage to equipment due to the occurrence of damage and damage to production due to equipment stoppage, abnormality diagnosis of equipment is widely performed. As an example of such a facility diagnosis technique, for example, “Completion of Technical Information on Facility Failure Diagnosis and Predictive Maintenance” (Fuji Techno System) is known.

[0003] Among the equipment diagnosis techniques, monitoring of sound and vibration is frequently used as a detection method for diagnosis of mechanical equipment such as a rotating machine. This is to determine the presence or absence of an abnormality in a mechanical unit such as a bearing based on the strength of a component related to a fundamental frequency f0 defined by the number of revolutions and the like.
The frequency characteristic (spectrum) of the signal waveform is calculated using frequency analysis means such as an FT (Fast Fourier Transform) analyzer, and the amplitude intensity at the target frequency is displayed or recorded. For the purpose of detecting the peak frequency, the point at which the spectrum calculated as described above becomes maximum is displayed or recorded as the peak frequency.

[0004] However, the frequency analysis means as described above
A discrete Fourier transform for discrete time series data,
The calculated spectrum is also for a discrete frequency sample, and depending on the operating conditions of the mechanical equipment, the monitored vibration component deviates from the frequency sample as described above, and a false report is issued that the level of the vibration component has been significantly reduced. There is fear.

That is, when discrete Fourier transform is performed with a frequency resolution of 0.1 [Hz] and a data length of 256 points, for example, an amplitude of 1.0 [V] and a frequency of 1.0 [H] as shown in FIG.
In the case of the vibration waveform of z], the peak value of the spectrum detects a correct value as shown in FIG. 13, but as shown in FIG. 14, even if the amplitude is 1.0 V, the frequency is 1.04.
In the case of a vibration waveform of [Hz], as shown in FIG. 15, the peak frequency becomes 1.0 [Hz], and the peak frequency also becomes
The component also detects an incorrect value. Further, the calculation resolution of the peak frequency is also limited to the frequency sample interval, and it is not possible to detect the peak frequency in more detail.

On the other hand, Japanese Patent Application Laid-Open No. Sho 58-219424 discloses
There is a rotating machine inspection device proposed in Japanese Unexamined Patent Application Publication No. HEI 9-86. In this method, the sum of squares of the frequency components is calculated over a frequency section having a specific width including the frequency component of interest, and is used as a substitute for the spectrum component monitor.

As a technique for analyzing the frequency characteristics of a waveform in detail, a zooming apparatus for an FFT analyzer is disclosed in Japanese Patent Application Laid-Open No. 63-196687. In order to obtain the same effect as lowering the sampling frequency afterwards, this technology performs stepwise half-band filter processing on time-series data preliminarily multiplied by a sine wave carrier to prevent aliasing. However, the spectrum calculation is performed after the data is thinned out. According to this technique, the frequency characteristics of the measurement signal can be obtained in detail, and the above-described problem of frequency deviation can be solved, and at the same time, the resolution of peak frequency detection can be improved.

[0008]

However, the one disclosed in Japanese Patent Application Laid-Open No. 58-219424 discloses the following.
Although it provides an alternative technique to the spectrum component monitor, it has a problem that the peak frequency cannot be detected.

Further, in the apparatus disclosed in the above-mentioned Japanese Patent Application Laid-Open No. 63-196867, in the case of zooming, a carrier signal generator and a multiplier are newly required, and the zooming operation according to a target frequency section is required. Complicated processing such as resetting of the carrier frequency and half-band filter processing is required, and the data length increases in accordance with the zooming magnification, so that the responsiveness of the frequency response calculation is impaired.

The present invention has been made in view of the above-mentioned conventional problems, and provides a signal waveform processing method and apparatus capable of analyzing in detail the frequency of measurement data and its frequency components with a simple configuration. The task is to

[0011]

SUMMARY OF THE INVENTION The present invention provides a complex signal in which a signal waveform is sampled at fixed time intervals, a signal sequence obtained by the sampling is used as a real part, and a Hilbert transform pair of the signal sequence is used as an imaginary part. Or a signal sequence obtained by the sampling as an imaginary part, and calculating a complex signal sequence having a Hilbert transform pair of the signal sequence as a real part, and calculating the argument of the complex signal at a predetermined data length. Calculating the frequency of the signal waveform based on the gradient of the series, and calculating the amplitude of the signal waveform based on the amplitude of the series of the complex signal at another predetermined data length, whereby the frequency of the signal waveform is calculated. Alternatively, the above problem is solved by calculating at least one of the amplitudes.

Further, according to the present invention, there is provided a signal waveform processing device, comprising: means for sampling a signal waveform at fixed time intervals; a signal sequence obtained by the sampling being a real part; and a Hilbert transform pair of the signal sequence being an imaginary number. Means for calculating a complex signal sequence having a Hilbert transform pair of the signal sequence as an imaginary part and a Hilbert transform pair of the signal sequence as a real part; Means for calculating the frequency of the signal waveform based on the inclination of the series of the argument of the complex signal, and calculating the amplitude of the signal waveform based on the amplitude of the series of the complex signal at another predetermined data length And means for performing the above.

A signal waveform x (t) of vibration or sound detected at or near the bearing portion of the rotating machine has a sine wave shape as shown in the following equation (1).

X (t) = A cos (2πf 0 t + ψ) (1) where f 0 is a frequency, A is an amplitude, and 初期 is an initial phase.

The time series data obtained by discretizing the signal waveform x (t) at a constant sampling time interval T is given by the following (2)
It can be expressed as an equation.

X (n) = A cos (2πf0 Tn + ψ) (2) Here, n indicates an address of time-series data.

According to the present invention, the amplitude A and the frequency f0 in the signal are detected with high accuracy.

For example, Oppenheim, shafer: "Digital
"Signal Processing", chapter 7, Prentice-
Using the discrete Hilbert transform as described in Hall, the time series data x obtained from the signal waveform
From (n), it is possible to generate a waveform as shown in the following equation (3) in which the amplitude is the same and the phase is different by 90 °.

Y (n) = Asin (2πf0 Tn + ψ) (3)

Therefore, a complex signal z (n) = x (n) + ji having x (n) as a real part and y (n) as an imaginary part.
(N) (j is an imaginary unit, that is, j ² = −1),
From the above equations (2) and (3), the following equations (4) and (5) are obtained.

F 0 = ｛(argument of z (n)) − ψ｝ / nT · 2π (4) A ² = | z (n) | ² = x (n) ² + y (n) ² (5) )

By using these equations, according to the present invention, the signal sequence x (n) obtained by sampling the signal waveform at regular time intervals is used as a real part, and the Hilbert transform pair y (n) is used. By calculating an analytic signal (complex signal) to be an imaginary part, the frequency f0 and the amplitude of the complex signal z (n) are obtained from the inclination of the argument of the complex signal z (n) (coefficient of a linear function component of time). The amplitude A of the original signal can be calculated.

As a method of forming a complex signal, y (n) may have a real part and x (n) may have an imaginary part as shown in the following equation.

[0024]

(Equation 1)

In this case, since the following equations (7) and (8) are obtained, the slope of the argument of the complex signal (the coefficient of the linear function component of time) is multiplied by −1 to obtain the frequency f. ₀ ,
Further, the amplitude A of the original signal can be calculated from the amplitude of the complex signal.

[0026]

(Equation 2)

[0027]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring now to the drawings, x (n)
Is a real part and y (n) is an imaginary part.
An embodiment of the present invention will be described in detail.

FIG. 1 is a block diagram showing a schematic configuration of a signal processing device according to the first embodiment of the present invention.

In FIG. 1, reference numeral 10 denotes a sensor generally used for diagnosing mechanical equipment, such as a piezoelectric vibration sensor that detects vibration or sound and converts it into an electric signal, or a condenser microphone. 12 is the sensor 1
This is a sampling device that samples an analog waveform of 0 (signal source) at regular time intervals and converts the signal waveform x (t) into time-series data x (n). A memory 14 stores time-series data x (n) obtained by sampling for a predetermined data length N, and a memory 16 performs a Hilbert transform process described below on the time-series data x (n). A first arithmetic unit that calculates the waveform y (n)
Is a second arithmetic unit for calculating a frequency from the time-series data x (n) and y (n), and 20 is a second arithmetic unit for calculating the frequency.
This is a third arithmetic unit that calculates the amplitude from (n) and y (n). Reference numeral 22 denotes a display device.

As the sampling device 12, for example, a commercially available A / D converter may be used, but its sampling time interval T needs to be set so as to satisfy a condition that does not cause aliasing. That is, for the frequency upper limit fmax of the signal to be observed, T <1 / (2fmax
) Must be set. Also, 1 / (3
fmax) or more.

Also, the memory 14 may use storage means that is generally widely used, and its data length N may be appropriately set according to the required operation speed. It is desirable to set 256 to N = 512.

The operation of the first embodiment will be described below.

The signal waveform (analog waveform) x (t) detected by the sensor 10 is sampled by the sampling device 12 at fixed time intervals, and the time-series data x
(N) and stored in the memory 14.

FIG. 2 shows the time-series data x (n) of the vibration waveform sampled in this manner.

The first arithmetic unit 16 is, for example, Oppenheim,
shafer: “Digital Signal Processing”, chapter
The discrete Hilbert transform pair y (n) of the time-series data x (n) is calculated by using a method described in r7, Prentice-Hall.

An example of the specific calculation method is as follows. Calculate the discrete Fourier transform of x (n) (the calculation result is defined as X (n)). 2. Calculate Y (n) defined by the following equation.

(Equation 3) 3. The discrete inverse Fourier transform of Y (n) is calculated (the calculation result is assumed to be y (n)). If the data length N is equal to a power of 2 as in the preferred embodiment, FFT (fast Fourier transform) can be used as the discrete Fourier transform operation.

FIG. 3 shows an example of the discrete Hilbert transform pair y (n) calculated for the time series data x (n) shown in FIG.

In this way, for example, the time series data x
A complex signal z (n) having (n) as a real part and time-series data y (n) as an imaginary part is obtained.

The second arithmetic unit 18 calculates the frequency according to the above-mentioned equation (4). The argument θ of the complex signal z (n) has periodicity as shown in FIG. Therefore, in the calculation of the frequency, the slope Δ = (θ2−θ1) / (n2−) of the appropriate data section [n1, n2] where the argument θ monotonically increases in the range of [−π, π]. n1) may be calculated, or a linear regression method may be used in the data section.

The third arithmetic unit 20 calculates the amplitude according to the above-mentioned equation (5). That is, the absolute value Z (n) = {x (n) ² + y (n) ² } of the complex signal z (n) is calculated for each time sample as shown in FIG. The amplitude A may be determined by the square root of. Since Z is a constant value irrespective of n, Z (ni) for any ni between 0 and N-1 may be set as the representative value. However, as in the present embodiment, the end of the waveform section is set. May be used, the average value of the data section appropriately selected only in the vicinity of the center of the waveform section may be used.

In this embodiment, the vibration waveform of the rotating machine bearing was specifically analyzed. The rotation speed of the machine was roughly 1 [rps], and the amplitudes of the vibrations were almost the same. However, the actual rotation speeds of the three measurements were 1.01 and 0.9, respectively.
8, 1.03 [rps], and the amplitudes predicted by different analysis means at each measurement are 1.25, 1.13,
1.38 [V].

The time waveforms of the vibration measured by the three measurements are as shown in FIGS. 6 to 8, respectively. FIG. 9 shows a result obtained by performing an arithmetic operation on these time waveforms with the sampling period of 0.1 [sec] and the data length N = 256 in the present embodiment. As shown in FIG. 9, all the measured values have an error within 0.3%, and it can be seen that they match with good accuracy.

Next, a second embodiment of the present invention applied to frequency detection will be described.

FIG. 10 shows a schematic configuration of a signal processing device according to the second embodiment.

The present embodiment is for detecting in detail the frequency of the detected analog waveform in detail. The signal processing device of the first embodiment shown in FIG.
The configuration is the same as that from which. Therefore, the operation is the same as that of the frequency detection calculation in the first embodiment described above.

Next, the third embodiment of the present invention applied to width fluctuation detection.
An embodiment will be described.

FIG. 11 shows a schematic configuration of a signal processing device according to the third embodiment. The third embodiment is for detecting the amplitude intensity of the detected analog waveform in detail, and is similar to the signal processing device of the first embodiment shown in FIG. 1 in which the second arithmetic unit 18 is removed. Be composed. Therefore, the operation is the same as that of the above-described calculation of the waveform amplitude in the first embodiment.

The second and third embodiments are specializations of the first embodiment for frequency detection and amplitude detection, respectively, and are simplifications of the first embodiment. Therefore, the frequency or amplitude can be detected with high accuracy with a smaller number of device configurations.

Also, it is a matter of course that the device can be constituted by using a complex signal in which y (n) is a real part and x (n) is an imaginary part.

In these embodiments, the components from the sampling device 12 to the display device 22 may be configured as individual devices, but may be modeled as elements on a microprocessor. Or,
The first, second, and third arithmetic units may be programmed, operated by the same or appropriate software, and output.

In a production site, it is expected that noise of a component other than the frequency of the sine wave to be observed is mixed.
A band-pass filter for blocking unnecessary frequency bands may be provided before the second processing unit, or a known digital filter processing for removing unnecessary band components may be performed before the first arithmetic unit 16. .

[0052]

As described above, according to the present invention,
Since the frequency and amplitude of the measurement data can be calculated with high accuracy, the alternative frequency component of the measurement target can be monitored in detail by frequency regression using the conventional discrete Fourier transform. When the sample point deviates, the component is not erroneously measured. Further, since complicated processing such as a carrier signal generator, a multiplier, and a repetitive calculation of a half-band filter required for the frequency zooming method is not required, the frequency and amplitude of the measurement data can be calculated with a simple device configuration and algorithm. At the same time, there is an effect that the amount of operation data increases in proportion to the zooming magnification, so that operation time is not required and data update time does not increase.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a schematic configuration of a signal processing device according to a first embodiment of the present invention.

FIG. 2 is a diagram showing time-series data generated by a sampling device in the first embodiment.

FIG. 3 is a diagram showing a Hilbert transform pair output by a first arithmetic unit with respect to the time-series data of FIG. 2;

FIG. 4 is a diagram showing the argument θ of the complex signal z (n) in the first embodiment.

FIG. 5 is a diagram showing an amplitude Z (n) of a complex signal z (n).

FIG. 6 is a diagram showing a time waveform of vibration detected by an analysis experiment of a vibration waveform of the rotating machine bearing in the first embodiment.

FIG. 7 is a diagram showing a time waveform of the vibration detected in the analysis experiment of the vibration waveform of the rotary machine bearing in the first embodiment.

FIG. 8 is a diagram showing a time waveform of the vibration detected in the analysis experiment of the vibration waveform of the rotary mechanical bearing in the first embodiment.

FIG. 9 is a table showing measurement conditions and analysis results in an analysis experiment of a vibration waveform of the rotary machine bearing according to the first embodiment.

FIG. 10 is a block diagram showing a schematic configuration of a signal processing device according to a second embodiment of the present invention.

FIG. 11 is a block diagram showing a schematic configuration of a signal processing device according to a third embodiment of the present invention.

FIG. 12 is a diagram showing a time waveform when a frequency of a signal matches a frequency sampling point in a conventional method.

FIG. 13 is a diagram showing a discrete frequency spectrum when the frequency of a signal matches a frequency sampling point in the conventional method.

FIG. 14 is a diagram showing a time waveform when the frequency of a signal does not match a frequency sampling point in the conventional method.

FIG. 15 is a diagram showing a discrete frequency spectrum when the frequency of a signal does not coincide with a frequency sampling point in the conventional method.

[Description of Signs] 10 ... Sensor 12 ... Sampling device 14 ... Memory 16 ... First computing device 18 ... Second computing device 20 ... Third computing device 22 ... Display device

Claims (2)

[Claims] 1. A signal waveform is sampled at fixed time intervals, a signal sequence obtained by the sampling is used as a real part, and a Hilbert transform pair of the signal sequence is used as an imaginary part. The obtained signal sequence is used as an imaginary part, and a Hilbert transform pair of the signal sequence is used to calculate a complex signal sequence having a real part.Based on a gradient of the argument of the complex signal at a predetermined data length, By calculating the frequency of the signal waveform, and calculating the amplitude of the signal waveform based on the amplitude of the sequence of the complex signal at another predetermined data length, at least one of the frequency and the amplitude of the signal waveform A signal waveform processing method characterized by calculating. 2. A means for sampling a signal waveform at fixed time intervals, a sequence of complex signals having a signal sequence obtained by the sampling as a real part and a Hilbert transform pair of the signal sequence as an imaginary part, or Means for calculating a complex signal sequence in which a signal sequence obtained by sampling is an imaginary part and a Hilbert transform pair of the signal sequence is a real part; and a gradient of a sequence of the argument of the complex signal at a predetermined data length. Means for calculating the frequency of the signal waveform on the basis of, and means for calculating the amplitude of the signal waveform based on the amplitude of the sequence of the complex signal at another predetermined data length, the frequency of the signal waveform Alternatively, at least one of the amplitudes is calculated.