JP2968537B2 - Phase analysis method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[Industrial application field] The present invention analyzes the phase of an arbitrary frequency component in one of periodic fluctuations and aperiodic fluctuations or a function in which these are mixed in, for example, vibration synchronization analysis. It is about the method. [Prior Art] Conventionally, analysis of a phase change of a frequency component of a function such as a vibration waveform is performed by, for example, a phase lock loop (phase lock loop;
PLL) and other analog signal processing. For example, Patent Registration No. 1362995 (Japanese Patent Publication No. 61-31412)
No.)｝. In this method, for example, a phase change of a specific frequency component of a vibration waveform generated from a rotating machine to be analyzed, which is proportional to a frequency of the rotation detection signal, based on a rotation detection signal of the rotating machine, is determined by an analog signal processing method. The calculation is performed and the result is displayed. [Problem to be Solved] However, in the above-mentioned conventional method, the frequency resolution in analysis is practically low, about 5 Hz, and is analog (continuous) data. Also had the problem that the usability was low. An object of the present invention is to provide a method for analyzing a phase change of an arbitrary frequency component in a function such as a vibration waveform with high accuracy.

[Means for Solving the Problems]

The subject is: (1) using the phase value of a discrete spectrum obtained by performing a plurality of discrete Fourier transforms of the same data length at fixed time intervals on the phase change amount of an arbitrary frequency component included in a function. In the required phase analysis method, arbitrarily determine the time interval that is the basis for calculating the phase change,
The frequency corresponding to the time interval used as the reference for the phase change calculation is a constant multiple of the frequency of the periodic signal used for the discrete Fourier transform after being divided or multiplied, and the constant is an integral multiple of the order resolution of the discrete spectrum. In some cases, from the frequency of the periodic signal and the arbitrary frequency component, a spectrum order of the arbitrary frequency component and a discrete spectrum to be determined are determined, and the discrete spectrum obtained this time is determined for the determined discrete spectrum. The phase change amount is obtained as the difference between the phase value of the spectrum and the phase value of the discrete spectrum obtained last time, and the phase amount corresponding to the fractional part of the ratio between the spectrum order and the constant is further reduced and corrected to obtain the arbitrary frequency. A phase analysis method comprising calculating a phase change amount of a component. (2) A phase analysis method for obtaining a phase change amount of an arbitrary frequency component included in a function using a phase value of a discrete spectrum obtained by performing a plurality of discrete Fourier transforms of the same data length at a fixed time interval. In, arbitrarily determine the time interval that is the reference for the phase change calculation,
A frequency corresponding to a time interval used as a reference of the phase change calculation is a constant multiple of the frequency of a periodic signal used for the discrete Fourier transform after being divided or multiplied, and the constant is not an integral multiple of the order resolution of the discrete spectrum. In this case, the spectrum order of the arbitrary frequency component is determined from the frequency of the periodic signal and the arbitrary frequency component, and the frequency order of the arbitrary frequency component is determined between two adjacent discrete spectra that cannot be represented by a discrete spectrum. , A discrete spectrum close to the arbitrary frequency component of the two discrete spectra is determined as a target discrete spectrum, and the discrete spectrum obtained this time is determined for the determined discrete spectrum. The amount of phase change is determined as the difference between the phase value of the spectrum and the phase value of the discrete spectrum obtained last time, and a positive value including the constant 1 A value obtained by subtracting and correcting a phase amount corresponding to a fractional part of a ratio of the order resolution of the discrete spectrum and a value closest to the determined spectral order by several times, and calculating a phase change amount of the arbitrary frequency component. Phase analysis method. (3) In the phase analysis method according to claim 1 or 2, the corrected phase change amount of the arbitrary frequency component is calculated a plurality of times, and each calculated phase change amount is -18.
A phase analysis method comprising: correcting a value in a range from 0 degrees to +180 degrees; calculating an average value thereof; and calculating the average value. Can be solved. [Function] Function (Hereinafter, time is taken as an independent variable as an example. That is, the function to be handled is a time series function.)
If is a continuous data, it is converted to discrete data, and then a discrete spectrum of the function is obtained by a discrete Fourier transform process having a fixed data length such as a fast Fourier transform (FFT). This processing is performed a plurality of times for the discrete data with a predetermined time shift. Then, for an arbitrary frequency component of the original function, a phase change amount after a lapse of a certain time, that is, at a certain time interval, is obtained as a change amount of a series of phase values related to a corresponding discrete spectrum. Further, a spectrum obtained by the discrete Fourier transform is digital data, and therefore, a function to be analyzed may include a true frequency component that cannot be expressed by the transform. The phase change amount of the true frequency component that cannot be expressed is calculated using the phase value related to the discrete spectrum that can be expressed by this conversion. Further, when the time interval cannot be represented by discrete sampling, the phase change amount of an arbitrary frequency component included in the function with respect to the time interval is calculated using a series of phase values related to a discrete spectrum converted in a fixed time. EXAMPLES Hereinafter, the present invention will be described in detail based on examples. FIG. 1 is a block diagram showing one embodiment of the present invention.
In the following, the function will be described by replacing the function with vibration. When the vibration is an analog signal, the vibration signal 5 input from the vibration signal input terminal 1 is used as a reference clock using a clock generated by the transmitter, and the periodic signal 6 input from the periodic signal input terminal 2 is divided and multiplied. The A / D conversion unit 3 performs conversion (A / D conversion) from an analog signal to a digital signal using the pulse signal generated thereby as a sampling timing. The vibration signal converted into a digital signal by the A / D converter 3 is converted into a discrete spectrum by a discrete Fourier transform such as FFT. In this conversion process, the length of the data group (the number of data) to be converted in each discrete Fourier transform is fixed, and the conversion process is repeated a plurality of times while shifting the range of the data group by a fixed time. Do. Using the plurality of discrete spectrum data generated in this manner, the phase analysis unit 4 analyzes the phase change of an arbitrary frequency component of the original vibration waveform by the following method. Here, a case where M discrete Fourier transforms are performed will be described. Then, as the phase change amount, the average change amount of the phase value regarding a certain discrete spectrum for each successive time is considered. Further, the amount of change is represented by the following (a) to (d).
Are obtained separately for the four cases. Note that Pi (−180 ° <Pi
≦ + 180 °; i = 1, 2,..., M) is a phase value related to a discrete spectrum of interest in the result of the i-th discrete Fourier transform. (A) The case where the spectral order (the frequency corresponding to one cycle of the periodic signal 6 in FIG. 1 is called primary, and the other frequencies are represented by multiples thereof) are integer orders. Phase change amount P′i (i = 1, 2,..., M
-1) is expressed by equation (1). P′i = Pi + 1−Pi (1) Next, P′i is converted into P ″ i by the equation (2) so that −180 ° <P′i ≦ + 180 °. P′i + 360 ゜ × n (2) where n is an appropriate integer, and the average change amount Pave of M−1 times to be obtained is expressed as in the following equation (3): Pave = (| P ″ 1 | + | P ″ 2 | +... + | P ″ M−1 |) / (M−1) (3) FIG. 2 is an example of a phase analysis result of a sine wave having a secondary frequency. I in FIG. 2 is an average waveform of a discrete spectrum that is a result of M (eight in this example) discrete Fourier transforms. Further, II in FIG. 2 is a graph showing the state of the change of the phase value with respect to the secondary spectrum for each time, and III in FIG. 2 is the average of the phase values for each time obtained from the equation (3). This is the amount of change and represents the degree of synchronization. As can be seen from FIG. 2, it can be said that the amount of phase change of this spectrum is small, and therefore the phase is stable. That is, according to the method of the present invention, it can be confirmed that the temporal variation of the sine wave is synchronized with the periodic signal. (B) When the spectrum order is other than the integer order. In this case, the phase change amount is obtained by the same method as in (a), but if the obtained value is somewhat smaller than the value corresponding to one sampling period, the phase change amount corresponding to the fractional part of the spectrum order is obtained. In order to correct the minute, the following equation (4) is used instead of the equation (1). P′i = Pi + 1−Pi−360 ゜ × (decimal part of spectrum order) ‥‥ (4) In this case, the phase relationship between the true frequency component included in the vibration and the periodic signal becomes In principle, discrete Fourier transform such as FFT is a measure to be taken because it cannot be recognized correctly. Here, the “phase value corresponding to one sampling period” Ps is a value represented by the following equation (5). Ps = [(spectral order) / (F × N)] × 360 ゜ (5) where N is the data length (number of sampling points) of a data group used in one discrete Fourier transform, and F is The order (frequency) of the discrete spectrum obtained by the discrete Fourier transform, that is, the order (frequency) resolution. For example, when N = 1024 points, F = 0.03125 order, and the spectrum order is 1.25 order, Ps = 14.0625 °. Further, “slightly smaller” cannot be determined because it depends on the performance of the A / D converter 3 and the like, but does not become larger than 1 / (M−1) of Ps. FIG. 3 is an example of a phase analysis result of a sine wave having a frequency of 1.25 order. I, II and III are the same as in FIG. Since the frequency is not of the order of an integer, this sine wave is not synchronized with the periodic signal, but this can be confirmed by the method of the present invention (III in FIG. 3). (C) The case where the time interval serving as the reference for calculating the phase change is R1 times the frequency of the periodic signal 6 in FIG. However, R1 / F is an integer. In this case, the following equation (6) is used instead of equation (1) in the method (a). P′i = Pi + 1−Pi−360 ゜ × {fraction part of (spectral order / R1)} (6) Similarly to the case of (b), the difference between the spectrum and the time interval used as a reference for calculating the phase change is obtained. This is a process to be performed because the phase relationship cannot be correctly recognized in principle by a discrete Fourier transform such as FFT. FIG. 4 is an example of a phase analysis result of a sine wave having a frequency equal to the time interval of 1.25 times the frequency of the periodic signal 6 as a reference for calculating the phase change. I, II and III are the same as in FIG. The sine wave will be synchronous with this time interval, and this can be confirmed by the method of the present invention. (D) The case where the time interval used as the reference for calculating the phase change is R2 times the frequency of the periodic signal 6 in FIG. However, it is assumed that R2 / F is not an integer. In this case, the following equation (7) is used in the method (a) instead of the equation (1). P′i = Pi + 1−Pi−360 ゜ × {fractional part of (R2 ′ / F)} (7) Here, R2 ′ is a spectrum order of interest among positive integer multiples including 1 of R2. It is the closest value. This correction is performed to calculate the phase change amount of the frequency component with respect to the time interval that cannot be expressed by the discrete sampling using the phase change amount regarding the discrete spectrum. FIG. 5 is an example of a phase analysis result of a sine wave having a frequency equal to the time interval whose time interval as a reference for calculating the phase change is 4/3 times the frequency of the periodic signal 6. I, II and III are the same as in FIG. The sine wave will be synchronous with this time interval, and this can be confirmed by the method of the present invention. [Effects of the Invention] As is apparent from the above description, according to the present invention, the phase change amount of any frequency component included in the function is obtained by a digital analysis method called discrete Fourier transform, so that the analysis accuracy is high. In addition, subsequent secondary processing such as data management becomes easy. Further, the true frequency component existing between discrete spectra that cannot be expressed by the discrete Fourier transform and the phase change amount of the frequency component with respect to the independent variable interval that cannot be expressed by the discrete sampling can be obtained by the method of the present invention. Therefore, for example, the periodicity analysis of vibration generated from a rotating machine can be easily performed.
Moreover, it can be performed with high accuracy.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an apparatus for implementing the method of the present invention. FIGS. 2, 3, 4 and 5 are graphs showing the results of phase analysis by the method of the present invention. FIG. 2 shows a case where the spectrum order is an integer order, and FIG. 3 shows a case where the spectrum order is an integer order. In the cases other than the following, FIGS. 4 and 5 show examples in which the reference interval for calculating the phase change is different from the original periodic signal. 1: Vibration signal input terminal 2: Periodic signal input terminal 3: A / D converter 4: Phase analyzer 5: Vibration signal 6: Periodic signal I: Discrete spectrum waveform of vibration II: Phase change graph for a certain spectrum III: Yes Phase change of spectrum

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Claims (3)

(57) [Claims] 1. A phase change amount of an arbitrary frequency component included in a function is obtained using a phase value of a discrete spectrum obtained by performing a plurality of discrete Fourier transforms of the same data length at fixed time intervals. In the analysis method, a time interval serving as a reference for calculating the phase change is arbitrarily determined, and a frequency corresponding to the time interval serving as the reference for calculating the phase change is divided or multiplied to obtain a periodic signal used for the discrete Fourier transform. When the frequency is a constant multiple and the constant is an integer multiple of the order resolution of the discrete spectrum, the frequency of the periodic signal and the arbitrary frequency component are used to determine the spectral order of the arbitrary frequency component and the discrete Determine the spectrum, for the determined discrete spectrum, the difference between the phase value of the discrete spectrum obtained this time and the phase value of the discrete spectrum obtained last time Calculating a phase change amount, further reducing and correcting a phase amount corresponding to a fractional part of a ratio between a spectrum order and the constant, and calculating a phase change amount of the arbitrary frequency component. Method. 2. The phase change amount of an arbitrary frequency component included in a function is obtained by using a discrete spectrum phase value obtained by performing a plurality of discrete Fourier transforms of the same data length at a fixed time interval. In the analysis method, a time interval serving as a reference for calculating the phase change is arbitrarily determined, and a frequency corresponding to the time interval serving as the reference for calculating the phase change is divided or multiplied to obtain a periodic signal used for the discrete Fourier transform. When the frequency is a constant multiple and the constant is not an integral multiple of the order resolution of the discrete spectrum, from the frequency of the periodic signal and the arbitrary frequency component, determine the spectral order of the arbitrary frequency component, When an arbitrary frequency component exists between two adjacent discrete spectra that cannot be represented by the discrete spectrum, the two discrete spectra Among the above-mentioned arbitrary frequency components is determined as a target discrete spectrum, and the phase value of the discrete spectrum obtained this time and the phase value of the discrete spectrum obtained previously are determined for the determined discrete spectrum. A phase change amount is obtained as a difference between phase values, and a value closest to the determined spectrum order by a positive integer multiple including the constant 1 and a phase amount corresponding to a fractional part of a ratio of the order resolution of the discrete spectrum are calculated. A phase change method for calculating the phase change amount of the arbitrary frequency component. 3. The phase analysis method according to claim 1, wherein the corrected phase change amount of the arbitrary frequency component is calculated a plurality of times, and each calculated phase change amount is calculated from -180 degrees to +180 degrees. A phase analysis method, wherein after correcting to a degree range, an average value thereof is obtained and calculated as an average change amount.