JPH02244205A - Fourier transforming device and fourier transforming method - Google Patents

Abstract

PURPOSE:To attain the real time analysis of a waveform by multiplying the new vibration waveform value by the small weight value according to the stored old mean vibration waveform and defining the new mean vibration waveform value with addition of the new vibration waveform when the new vibration waveform value is stored in a mean vibration waveform value area at the corresponding time for each sampling cycle. CONSTITUTION:The newly sampled vibration waveform value is stored in a memory of the corresponding order with the time mean addition of the memory. Then N pieces of new complex amplitude value Ck' are obtained via an equation 1 in a range covering K = 0 through N - 1 for each sampling of a vibration waveform based on the old complex amplitude value Ch already obtained as well as the difference between the new mean vibration waveform value -Xin and the old mean vibration waveform value -Xout so far stored. Then these values Ck' are updated. Thus it is possible to obtain a high speed controller which is immune to the noises and errors and can extremely shorten the calculating time.

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention relates to fast Fourier transform (FFT), which is widely used as a vibration waveform analysis device.

Processes human waveforms in real time for each sampling period,
This invention relates to a Fourier transform device and Fourier transform method as a controller that can output in real time.

[Conventional technology]

J of discrete Fourier transform (hereinafter referred to as rI, abbreviated as F'rJ)
An outline of a frequency analyzer (hereinafter abbreviated as r F F 1' analyzer) using IK theory will be explained with reference to FIG. Read the waveform values for the number of memories (generally discussed as N samplings, but here we will exemplify the case of 8 samples from beginning to end. Expansion to N samples will be omitted) in a specified sampling period, and This is step 1 of the flowchart shown in Figure 3.The stored values are xo, X1# X!y X8+ x4.X!I* in this example.
xe, x'y'' (+).

Using these sampling values, in step 2, D FT
The values after OF'T to be processed are Ao, As,
Ax, As, Aa+ Ass AS, A7
-(2) and the eight values of aAh that are found are generally complex numbers, and how to find them is according to the following formula.

% formula % However, j = to r: 〒 = imaginary unit This value of Ah means the compound J4 amplitude for each frequency ω, and the larger the value of Ak, the more prominent the vibration of that frequency It is shown that.

Next, in step 3, the absolute value of the calculation result Ak (k = O~7) is displayed as a bar graph on the display.

The 1° analyzer performs at high speed the series of operations of data acquisition, DFT processing, and display representation shown in steps 1 to 3 in FIG.

The timing of this series of processing is shown in FIG. A D F T calculation is performed on waveform values that are intensively captured for each section of the original vibration waveform.

Data acquisition is stopped while the DFT is being calculated and displayed on the display.

Therefore, not all sections of the input waveform are subjected to DFT calculation, and it is inevitable that some sections will be overlooked.

1) The FT calculation assumes that the values of the captured data X0-X7 are periodic functions that are periodically repeated even outside the interval. For that, input value XO−”
Instead of calculating the actual value of X7 using DFTFT, a value multiplied by a window function is usually used. Further, as the algorithm for determining the complex amplitude Ak shown in the definition formula (3), a very high-speed algorithm called butterfly operation is adopted.

As described above, various techniques have been devised in actual Fourier transform devices. Examples of these conventional Fourier transform devices include the device described in Japanese Patent Application Laid-open No. 196370/1983.

As mentioned earlier, the normal )'? ” With the 'l' analyzer, there was a pause period in data acquisition between the first data acquisition and the next data acquisition.This FFT analyzer displays and monitors the frequency analysis results of the vibration waveform. Since the main purpose is to monitor the complex amplitude value of each frequency component displayed as the output, it is acceptable to have such a pause period to detect the occurrence of abnormal vibrations and analyze their causes. F'' because you can get useful information for non-electronics
F"1" analyzers are widely available.

By the way, in order to eliminate the above-mentioned pause period, DFT processing is performed every time one piece of waveform data is captured.

The calculation formula for calculating the complex amplitude value is also available in the literature (Takeshi Yasuoin).

Written by Masayuki Nakajima (r)' How to use 'r', Electronic Science Series 91, Sanpo Publishing, February 15, 1982, page 132
~133).

The calculation formula will be explained for the case where the sampling value is 8M.

Now, at a certain time t, past eight pieces of waveform data X
m is in memory XOy Xle Xzt XOy Xis 1
6g Xll@
4. As4 A41 All AIIg A7
...Assuming that (6) is given, when a new waveform data value xs is read after one time t+Δ, the contents of the waveform data storage memory are XIHXIHX8g X4g X8# Xay X7#
XA...'(7) is updated. So is there a new one that corresponds to this? 6i elementary amplitude value A h' as Ao'1A1'HAM'pAB'#A
4' , A6' , AB' , A7' ”・(
8) We will look for a method to obtain it in the form.

The complex amplitude value A corresponding to the waveform data value of Equation (5) is for k=o~7 according to the definition of Equation (3), and similarly corresponds to the waveform data value of Equation (7). The new complex amplitude value Ah' is given by the following equation.

for k-0~7 Comparing both equations (9) and (10), the following equation is obtained.

for k=o~7 What the above formula means is that the waveform value is read every moment and every sampling time as shown in Figure 4,
That value goes into memory. Let it be xln (=xa), then the oldest data in memory must be discarded, which is Xo□ (x=xo).

When the number of sampling waveform data is N, the complex amplitude value Ak can be updated using the following formula for k=o~(N-1). In this way, the waveform data is sampled one after another without any pauses in data acquisition, and the complex amplitude value on the open side is obtained from time to time each time. This is the processing principle of continuous DFT.

[Problem to be solved by the invention]

Since the main function of the FFT analyzer in the prior art described above was monitoring, between the first N data sampling acquisition and the next N data sampling acquisition as shown in FIG. There was a pause in data import. N
The pause period for each data acquisition operation is the time required to calculate D F T and display the calculation results.

In a normal FFT analyzer, interruption of the data acquisition operation described above is unavoidable. This is sufficient as a monitor, but when used as a control device, interruption of data acquisition is not allowed. 11. The control device is required to have a continuous algorithm that takes in data at y times and performs the D F TIB process each time.

On the other hand, the above-mentioned formula 12 has also been proposed as an algorithm for continuous DFT processing.

By the way, 1) FT calculation in the FFT analyzer is based on the premise that the captured data is a periodic function that is periodically repeated even outside the sampling interval (FFT window interval). That is, as shown in FIG. 5, the portion of the input waveform outside the sampling period is a periodic function in which the waveform within the sampling period is repeated. If, as shown in FIG. 5 (1), the sampling interval (window interval of F' F T) coincides with the period of this function, then the input waveform is transformed into a complex amplitude value, When the waveform whose phase is further advanced by 90 degrees is expressed as a real-time waveform by inverse Fourier transform, a waveform whose phase is advanced by 90 degrees with respect to the waveform of E is obtained.

However, as shown in Figure 5 (2), in the case of a periodic function with a period that does not match the sampling interval, the complex amplitude value is determined from the captured waveform, and then the phase is advanced by 90 degrees and the value is Fourier inverted. When converted back to real time waveform,
It is not always possible to obtain a waveform whose phase is 90 degrees ahead of the previous waveform.

The purpose of the present invention is to continuously capture waveform data at regular sampling intervals for components of the original signal that are synchronized with the sampling data capture period (FFT window section). It is an object of the present invention to provide a Fourier conversion device or a control device that can perform processing corresponding to a control law after DFT processing and continuously output a control signal at a prescribed sampling period by Fourier inverse transform.

[Means to solve the problem]

In order to achieve the above object, the present invention basically consists of the following configuration.

(1) Sampling interval (FF 'I) from input waveform
To extract periodic function components synchronized with the window interval of '.

(2) Perform continuous D F T processing on the obtained periodic function to obtain the complex amplitude value of the input waveform.

(3) A certain processing corresponding to a control law is applied to the obtained complex amplitude value for each frequency component.

(4) Perform inverse Fourier transform on the processed complex amplitude value,
Outputs a certain value as a control signal.

The above object is achieved by a control device constructed using such a method.

The first feature of the present invention is to store a predetermined number of vibration waveform values obtained by reading the vibration waveform at each sampling period. At that time, averaging processing is performed so that only the vibration waveform value of the periodic function component is obtained. In other words, when the new sampled vibration waveform value is stored in the vibration average waveform value area at the corresponding time for each sampling period, the storage The old vibration average waveform value is multiplied by a smaller weight value, and the new vibration waveform value is added to define the new vibration average waveform value.

For each such sampling period, the sampling interval (
It is characterized by the operation of averaging the human force vibration waveform values at corresponding times within the FFT window section to obtain a periodic function.

A second feature of the present invention is that a new complex amplitude value is determined from the difference between the old vibration average waveform value and the obtained new vibration average waveform value and the old complex amplitude value that has already been determined. be. Such searching DFT processing allows a significant reduction in calculation time, and is characterized by the ability to create a high-speed control device.

A third feature of the present invention is that a control circuit having arbitrary transfer characteristics can be obtained. That is, the amplitude is increased or decreased for each frequency component with respect to the complex amplitude value of the human waveform. It is also possible to advance or retard the phase by 90 degrees as desired without changing the gain.

Therefore, a control circuit having desired transfer characteristics can be obtained.

[Effect]

Continuously captures vibration waveforms at each sampling period,
A storage unit is provided to store the average value.

FIG. 6 shows a case where the storage section has eight memories. All contents stored in the storage section are initially 0. When starting in this state, after the vibration waveform is continuously captured eight times at each sampling period, the contents of the storage section become x volume = xt for i = 0 to 7. The contents of the storage section are now completely filled and the first period of sampling ends.

When the 9th data sampling of the vibration waveform is performed, xo' is taken in, and the contents of the storage section are X0=xo+
xo' t Xls xz, "'t Only the corresponding xo area is rewritten by X7. Then
After the second data sampling, XI' is taken in, and the contents of the storage section are xo, xt::xt+xo', x
Only the Mar area is rewritten by x, , -X7.

This operation is repeated, and after the 16th data sampling of the vibration waveform, X7' is captured and the contents of the storage section are: XOg X1e xz, 1llll+, X7"!?
+X7' rewrites the x7 area. When this 16th vibration waveform sampling is completed, the second period of sampling ends, and all the vibration average waveform values stored in the first period are replaced with new vibration average waveform values. That means that.

At the 17th data sampling of the vibration waveform, the third period begins, xo' is taken in, and the xo area is rewritten as the contents of the storage section, and X0=XO+XOg xz, X error "'g
It becomes X7.

In this way, when the vibration waveform Xs is sampled at a certain time, only the vibration average waveform value 71 is updated from the old vibration average waveform value to the new vibration average waveform value. Continuous DFT processing focusing only on change components is possible.

That is, when the vibration waveform is sampled, X is removed from the stored vibration average waveform value, and xl is newly defined. If the newly defined Xt is written as Xim, then the inside of the memory section will be as follows, and the contents of the memory will only change in one place.

Therefore, except for Xt, the data from XO to x7 still remains in this storage section, so the newly incoming X 1 = X s n and the outgoing Xt = Xo
If Fourier transform is performed using ut, the calculation can be performed using a simple transformation formula. This simplification of the transformation formula improves the processing speed, and therefore it becomes possible to complete the Fourier transform calculation process within the sampling time until the next sampling.

〔Example〕

Hereinafter, one embodiment of the present invention will be described with reference to FIG. - The case where the number of samples in the film is N will be explained.

The memory areas to be prepared include a real number area of KO""XN-1 that stores averaged waveform data, that is, periodic function components, and a complex amplitude value Ck (k=o
~N-1) and the area for storing them.

Area of complex amplitude value Bk (k=o~N-1) processed according to control law in frequency domain based on Ck, and Bk
This is the control signal V obtained by performing inverse Fourier transform on .

Next, when the i#th (i=0 to N-1) data xt of the waveform is sampled,
Since the contents of s are updated data, Xo1=Xs
Store it in X0ut as . Then, using the old average value waveform data 71 and the newly sampled waveform data x1, averaging processing of the i-th waveform data, that is, extraction of the periodic function component, is performed according to the following equation.

1+2M Store this in the X1m area and the X, area. This is step #1. Here, M is a number counted up for each sampling period.

Next, in step #2, the incoming average value data Xsm and the average value data to be discarded. Using Ilt, the contents of the complex amplitude value Ck are updated using the following equation called continuous form real-time FFT.

2 π for K-=O~N-1 However, ω*= □K In this way, the average value waveform data area XO~XN"'
The Fourier transform value Cm for each frequency is determined for the waveform stored in 1.

Next, in step #3, a complex amplitude value Bh is calculated by processing Ck according to a certain control law1.For example, the displacement signal
``'When calculating the Fourier transform value of velocity for XN-1, Bm=jωhCk+ for K=O~N 1
” (15), and all other types of processing are possible.

Bb=j Ckfor K:O~N1-(
16), it is possible to obtain a complex amplitude value with a phase lead of 90 m without changing the gain. In any case, according to a certain rule, the control signal is duplicated! l amplitude value Bk is defined. Generally expressing the rule as α1, Bk=ahCh for K=O”N-1-(17
) to obtain the frequency domain representation of the output signal.

Next, in step #4, Bb is subjected to inverse Fourier transform to express the frequency domain Bh to a real-time waveform, and at this time, a control signal vt at the sampling time corresponding to the input waveform value xI is output. The control signal v1 is obtained by the following equation.

At the same time as the control signal v is output, a counter i is counted up in order to take in the next waveform data.

The counter i starts from the initial value O, and is cleared to zero when i≧N (N is the number of samplings). In this way, the counter i repeats the value 0-N-1, and the number of samples never exceeds N. Therefore, each time one piece of waveform data is sampled, one control signal for that waveform data is output. Become. At the same time as the counter i is cleared to zero, the counter M in equation (13) is counted up. 0M starts from the initial value O and is counted up every sampling interval, and becomes a larger value as long as waveform data sampling continues.

By repeating the processing of steps #1 to #4 for each sampling period of waveform reading, the Fourier transform value Ck and the input average value waveform corrected by the averaging process of the waveform data x dung, that is, the extraction of the periodic function component Xi. A control signal v1 for data x1 is obtained.

This process will be specifically explained using FIG.

A case where the number of samplings N is eight will be explained.

First, the prepared average value waveform data area
7 and the area of complex amplitude value Ck (K = Q - 7) is cleared to zero. When a vibration waveform is read at a certain sampling period, averaging processing, that is, extraction of periodic function components, is executed, and the vibration average waveform value is stored in the average value waveform data area.

When the waveform data xo is read in FIG.
2°"xo+xo x' according to the definition of the formula.

1+20 2 is required. This is Xln and average value waveform data XO
The contents of sXo to be stored in the area are stored in the Xout area in advance.The series of operations shown in Figure 1 continues.When this is repeated eight times, the values are stored in the average value waveform data area in order. Ru. Using these 8 average value waveform data, the complex amplitude value Ck (K=0 to 7) is calculated by Fourier transformation.
is required. Ch (K=O~7) can be written as follows by the definition of Fourier transform.

However, ω, = -, ni = O ~ 7... (19)
One new piece of waveform data xo' in the next sampling period
is read and the old average value waveform data x.

As shown in the following equation, averaging processing, that is, extraction of periodic function components is performed using xl and stored in one area.

At this time, the old average value waveform data KO is X. ut, and the newly obtained average value waveform data is stored in xo.

This is the process corresponding to #l in FIG. Here, to distinguish it from the old average value waveform data.

If the new average value waveform data is written as xo', the average value waveform data area is xo 1 xt, X z, X1ll
xa, XBy Kg+ X7. When Fourier transform is performed using these average value waveform data, the complex amplitude value Ck' (K=O~7) is determined as follows.

Also, in the first sampling period, one new piece of waveform data XI' is read and new average value waveform data x, I is determined using the old average value waveform data x1 according to the following equation.

At this time, the average value waveform data area is XOg XI m K! *xa, x4
．． 1B, xs, X? becomes. When Fourier transform is performed using these average value waveform data, the complex amplitude value Cm
'(K=O~7) can be found as follows.

for K=O~7
-(20) Comparing equation (19) and equation (20), the following equation is obtained.

No' KO-0j (+J++ Ck' =Ch+ e fo
r K=O~7-(21) for K=O~7
- (22) No. (20)
) and equation (22), the following equation is obtained.

for K=O~7...(23) What the expressions (21) and (z3) mean are:
This means that the contents of the average value waveform data area are replaced with the old and new contents corresponding to the waveform data read at each sampling period, and the new complex amplitude value C, is corrected by the two old and new average value waveform data. This is # in Figure 1.
This is the second process.

Furthermore, a complex amplitude value Bh (K=O~7) processed according to a certain rule is defined corresponding to #3 in FIG.

Finally, the complex amplitude value Bh (K=0
~7) Perform inverse Fourier transform to obtain one frequency domain B k
(K = O~7) is transferred to a real-time waveform. At this time, for example, when waveform data xO is sampled, a control signal vo at that sampling time is output. The control signal vO is obtained by the following equation.

When the control signal vo is output, the data read counter i
is counted up by one, and a control signal v1 is outputted according to the following equation, corresponding to the sampling time of the waveform data XI' at which the next waveform data XI' is read.

In this way, the processes of flowcharts #1 to #4 in FIG. 1 are repeatedly executed, and from xo'! ? ' up to 8
When the processing of the waveform data is completed, the process moves to the first sampling period. At the same time, the waveform data is averaged, that is, the periodic function component is extracted (# in Figure 1).
1) The value of the counter M in the equation is incremented by one.

As a result, the periodic function component X1n in the sampling period can be used as a digital controller that outputs the control signal V using human power. The control law is based on the complex amplitude value Ck
This is reflected in how the processing from Bh to Bh is carried out. This means that how to determine α challenge is important for skillful control.

Since the periodic function component of the input vibration waveform is Fourier transformed in this way, its complex amplitude value can be processed in various ways, and the time at which the vibration waveform was sampled can be determined by inverse Fourier transform of the processed complex amplitude. Obtain the value corresponding to as the output value. It is also possible to use this output value as a control signal.

In this case, the complex amplitude in the frequency domain can be processed into any shape, so it is possible to create input/output functions with a greater variety than that specified by conventional transfer functions, which makes the control method more sophisticated. There is a certain effect.

By the way, there is a certain relationship regarding the complex amplitude value Ck obtained by Fourier transforming the input real signal Xms.

That is, Co = constant Ch = C (N - t) - x + z conjugate relationship CN = real number If we pay attention to these contents, it is possible to reduce the area of Ck to about half of that of 0.

Accordingly, the Fourier transform equation (Equation (14)) can also be simplified.

Also, the complex amplitude B h which is the Fourier transform value of the output signal V
(K = O'' N -1) is also half the area. Accordingly, the Fourier inverse transform equation (18) can also be simplified.

[Effects of the Invention] According to the present invention, it is possible to perform averaging on the complex amplitude values Ck, which has the effect of increasing resistance to noise and errors.

[Brief explanation of drawings]

Fig. 1 is a flowchart of an embodiment of the present invention, Fig. 2 is a function and time timing diagram of a conventional FFT analyzer, Fig. 3 is a flowchart of a conventional Fourier transform, and Fig. 4 is a conventional continuous Fourier transform. timing and algorithm, 5th
The figure shows the relationship between the period of a periodic function and the sampling interval. Figure 6 is a diagram explaining an embodiment of the present invention regarding changes in the storage unit each time data is taken in. Figure 7 is an embodiment of the present invention. FIG. 3 is a diagram illustrating an example of data acquisition and averaging processing. Figure 1■ Figure 1Kunifuzumandai Figure

Claims (5)

[Claims] 1. In a Fourier transform device that stores a predetermined number of N vibration waveform values obtained by reading the vibration waveform at each sampling period, and obtains a complex amplitude value C_k by Fourier transforming the vibration waveform values, the vibration waveform value storage memory is stored at a reference period. The newly sampled vibration waveform value is stored in the memory in the corresponding order by time average addition in that memory, and the newly obtained vibration average waveform value ■_i_n and the previous one are stored. Every time the vibration waveform is sampled from the difference between the old vibration average waveform value ■_o_u_t and the old complex amplitude value C_k that has already been obtained, a new complex amplitude value C_k' is calculated as C_k'=C_k+{(■
___i_n−■_o_u_t)/β}e−ij{(2π)
/n}・k However, from 0≦i≦N−1, the Fourier transform method is characterized in that N values from k=0 to N−1 are obtained and updated. 2. In the Fourier transform method according to claim 1, β=N
Alternatively, a Fourier transform method is characterized in that a convenient value such as β=√N or β=1 is selected as appropriate. 3. A Fourier device that includes a storage unit that stores a plurality of vibration average waveform values obtained by reading vibration waveforms at each sampling period and performing averaging processing, and a calculation unit that performs Fourier transform on the vibration average waveform values to obtain a complex amplitude value. In the conversion device, the old vibration average waveform value stored in the storage unit is updated to a new sampled vibration average waveform value, and the calculation unit updates the updated vibration average waveform value and the old vibration average waveform value. A Fourier transform device, characterized in that the Fourier transform method according to claim 1 or 2 is used to calculate the difference between the two values. 4. a first storage unit that stores a plurality of vibration average waveform values obtained by reading the vibration waveform of the controlled object at each sampling period and averaging the read waveform values; and a first storage unit that stores a plurality of vibration average waveform values obtained by averaging the read waveform values; A Fourier transform device comprising: an arithmetic unit that calculates a complex amplitude value; a second storage unit that stores the complex amplitude value; and a control unit that determines and outputs a control signal for the controlled object from the complex amplitude value. The old vibrational average waveform value stored in the first storage unit is updated by storing the sampled new vibrational average waveform value, and the complex amplitude value stored in the second storage unit is updated by storing the new vibrational average waveform value. 3. A Fourier transform device, characterized in that the Fourier transform method is corrected by the Fourier transform method according to claim 1 or 2, depending on the difference between the vibration average waveform value and the old vibration average waveform value. 5. In the device according to claim 4, when the number of vibration average waveform values stored in the first storage unit is N, the number of complex amplitude values stored in the second storage unit is N/2. A Fourier transform device characterized by: