PL235633B1 - Method for measuring frequency of vibrations - Google Patents

Description

Description of the invention The subject of the invention is a method of measuring the vibration frequency, used in the diagnostics of medical devices. mechanics, in particular automotive diagnostics.

One of the essential elements of the recorded signal waveform is the main harmonic component of the vibrations. It testifies to the main process related to the work of devices.

Analysis of vibroacoustic signals is one of the more frequently used methods of diagnostic devices mechanical, occurring also in car diagnostics. You can distinguish? indirect measurements, based on vibrations spreading in the air (sound measurements) and direct measurements of vibrating mechanical elements. Measured signal? harmonic can be analyzed in terms of: amplitude (equated with signal intensity), frequency spectrum, shift phase or other information contained in the signal. Among the examples of applications vibroacoustic analysis in the automotive industry can be mentioned: sound coming from the car engine to determine the intensity of the sound, analysis of sound from a car engine to determine the current rotational speed (for example, when testing the exhaust gas composition), sound coming from the work of the bearing to identify possible damage, analysis the course of the position of the plate forcing the vibrations of the suspension system in order to assess the effectiveness of damping (experimental work).

It often happens that the most important element of the recorded waveform is the main harmonic component of the vibrations. Dominant frequency because it testifies to the main process related to the work of device and allows you to track your device its course.

Among the commonly used methods of determining the main harmonic component, there are the ones you analyze? signal? in the time domain and those that work? in the frequency field. Among the analysis-oriented methods? in the time domain, it is worth mentioning: methods based on the autocorrelation function together with derivative methods, methods examining zero crossings or other features of the local value change over time. On the other hand, the analysis methods carried out in the field of frequencies are based on si? on the Fourier transform. The greatest popularity? enjoy si? the latter methods. You can mention among them? both advanced algorithms based on comb analysis or subspace analysis, as well as a simple search for the global maximum of the power density spectral function. However, in all such calculations the key element is the Fourier transform or its modification in the form of Fast Fourier Transform. Below I will stay the basic problems related to the above-mentioned most popular calculation methods are presented and their comparison with the presented algorithm. Commonly used algorithms for the determination of the harmonic frequency components are related to two limitations, the first of which is the complexity of numeric algorithm. The basic solution, which is the Fourier transform, is characterized by complexity numeric growing? together with the square of the number of samples of the signal under analysis, which in some cases excludes the use of this algorithm. Commonly used modification of the above solution, called quick transformation? Fourier, reduces the complexity of computational and addictive her? from value: Image available on "Original document" where N is numbers? samples of the analyzed signal. However, this solution is only possible for N-values that are a power of? number 2, what also? can be troublesome. Contrary to the aforementioned solutions, the proposed algorithm is characterized by linear dependencies? computational complexity in relation to the number of N (analyzed signal samples), which is definitely a better solution than the existing ones.

The second problem in commonly used algorithms is the accuracy of a calculation which depends on the ratio of the frequencies present in the analyzed signal to the sampling frequency and the number of analyzed signal samples. The Fourier transform (fast and ordinary) is characterized by the highest accuracy at frequencies close to a quarter of the signal sampling rate. The frequency range for which the accuracy face? is satisfactory, it depends on the number of analyzed signal samples. This is a big limitation, especially in the case of non-stationary signal analysis (where the frequency may change over time). The important thing is then? conducting the analysis for the smallest number of samples, but the this with a reduction in the accuracy of calculations, mainly at low frequencies. The proposed algorithm has a completely different? characteristics? the accuracy of the calculations. It works preferably at low relative frequencies - close to one tenth of the measured frequency to sampling rate ratio and is not sensitive to reducing the number of samples analyzed as long as they include they are at least three-quarters of the period of the main harmonic. This makes the proposed algorithm the most accurate in conditions where popular algorithms stop working. was? useful.

On the other hand, in terms of frequencies at which the Fourier transform shows the highest accuracy, the proposed algorithm is characterized by significant deterioration of accuracy. Therefore, the presented algorithm should not be considered as more accurate in a universal sense, but as a method of checking? si? better for specific applications (at lower frequencies of the signal tested and with fewer signal samples).

In relation to the presented algorithm, there are as? two limitations. The first is the fact that it does not determine the entire spectrum of harmonic components existing in the analyzed signal, but gives one value, corresponding? frequency of the main harmonic component. The second limitation is the sensitivity of of the algorithm for the existence of other harmonic components in the signal apart from the main component. The fact of their existence in the signal in proportion to the main component exceeding ten times percent limits the frequency range within which the major harmonic is correctly detected. Still ?? however, it is a relatively low frequency range in which the Fourier transform causes greater calculation errors than presented method.

From the description of the Polish invention application under the number P.402801 entitled "The method of determining the value of the effective vibration velocity", there is known the method of determining the value of the effective vibration velocity, which characterizes si? that? e is registering? with a sensor the acceleration signals vibrate? the object undergoing the diagnosis of the technical condition. Collected signals after conversion to the form digital is being processed in the converting device in successive steps. First it modifies? the collected acceleration signals vibrate? by znan? timezone functions. Then complements known? methods? number ?? of recorded signal samples to a number that is a power of the number two by adding zeros at the end and the beginning of the signal. Further modifies? the converted signal accelerate by determining the spectrum? vibrate, preferably using the known FFT algorithm. Then, based on the spectrum obtained in this way, it will accelerate? vibrates? the converted signal in the frequency domain for determining the frequency spectrum of the vibration velocity. Finally, based on the frequency spectrum, the speed then the value of the effective vibration velocity is calculated? a converted signal.

However, from the patent description after Pat. 207478 under the title "How to measure vibrations? and move? objects and a device for measuring vibrations and move? objects ", there is a known solution that with the use of three lasers one generates three coherent laser light beams, each one about a different length of light, which is combined with in the first coupler and in the second coupler the combined bundles are divided into two beams-a beam measurement and a bunch of reference, then bundle measurement is guided by on the tested object, until the light scattered on the tested object in the third coupler connects to the with a bunch of reference and given? detection in three photodetectors. Electrical signals from photodetectors are amplified in an amplifier and demodulates in demodulators. The amplitude of the signal after demodulation is proportional to the value of the vibration speed of the object, then on the basis of the demodulated signals, the the specter is vibrating? for individual axes, the values of vibration velocity components point in three axes and values of displacement and acceleration components in three axes.

The object of the invention is to develop a new method of determining the dominant frequency in a signal. The principle of the method is based on on comparing the signal amplitude with the amplitude its derivative and is characterized by ma ?? complexity numeric calculations? The results of its application have been compiled with the used data. commonly transform? Fourier. As it has been shown, at low frequencies and with short sections of the analyzed signal, it allows to increase the accuracy of the calculations. compared to traditional methods of determining the main harmonic component.

The method of measuring the vibration frequency is characterized by that? e for help? sensor is made measuring the course of the variation of a given physical value, preferably a position or acoustic pressure from a reference value, which is converted to on signal? digital, being a carrier of obtained results, signal this one passes on into the memory of a computer device, into a calculation block, in which this signal, being the carrier of the obtained results, is in parallel, then from this? signal from the obtained values using? a mathematical algorithm computes derivative of the obtained values, the values of the original results and the values of derivatives are successively determined amplitude, then determine the frequency oscillation? which is directly proportional to the amplitude of the signal derivative and inversely proportional to the double product of the constant? and signal amplitude, the obtained result is presented in a result block, preferably on the screen of the computer device.

Preferably, to the computation block is transferred signal? as a real-time result carrier or signal? historical stored in the memory of a computer device.

Preferably, the external sensor is a sensor of any physical size, in particular a strain gauge or a vibration sensor. waves caused? acoustic.

The presented method of determining the main harmonic component of a signal can be found in application in all kinds of detection systems operating in real time that require determining the frequency of how? move si? movable elements for devices. In such solutions, devices generate down?? a clear image of the main harmonic component against the background of other components. The advantages of this solution are: - possible ?? application in the analysis of relatively short waveforms (consisting of a few samples), - relatively high accuracy face? with a small number of samples, - relatively high accuracy face? at low frequencies (relative to the sampling frequency), - relatively little complex? numerical (even compared to Fast Fourier Transform), - thanks to the above features - the possibility of real-time monitoring of frequency changes.

With regard to the above applications, the presented algorithm can analyze signals of various origins, both sound, vibration and other. It should be noted, however, that the most optimal frequency for which the application of this method is justified, oscillates around one tenth of the sampling frequency. For the examples considered, the frequency of the sampling rate was 1000 Hz, and thus close to 100 Hz the calculation results proposed? methods? were the most accurate.

The subject of the invention was described in the embodiment example in the drawing, in which Fig. 1 shows the waveform of the harmonic signal x (t) for a frequency of 80 Hz and 32 samples, Fig. density power for the signal with a frequency of 80 Hz and 32 samples, Fig. 3 is the waveform of the harmonic signal x (t) for the frequency of 80 Hz and 16 samples, Fig. 4 is the spectral density power for the signal with a frequency of 80 Hz and 16 samples, Fig. 5 is the waveform of the harmonic signal x (t) for the frequency of 80 Hz and 8 samples, Fig. 6 is the spectral density power for a signal with a frequency of 80 Hz and 8 samples, Fig. 7 shows the dependence the relative error of the main signal frequency for 32 samples, Fig. 8 depicts the dependence of the relative error on the main signal frequency for 16 samples, Fig. 9 shows the dependence of relative error on the main signal frequency for 8 samples, Fig. 10 depicts the dependence of relative error from the main signal frequency for 32 samples, with the presence of additional harmonic components, Fig. 11 shows the range of usefulness of the presented method in the field of the main part of the signal. the frequency of the signal and the amplitude ratio of the additional harmonic to the main component, Fig. 12 is a block diagram illustrating the method according to the solution.

The method of measuring the vibration frequency is characterized by that? e in real time using? sensor (Cz) that measures the vibration waves caused? acoustic is measured course of the variability of the set physical value, vibration acceleration? from the reference value. The obtained values are converted into on signal? digital carrier of the obtained results (W). Signal? this one passes on to the memory of a computer device (K), to the computation block (BO) where is this signal? results (W) are separated by parallel to the channels (K1) (K2). Then from the channel (K1) the signal from the obtained values (W) using a mathematical algorithm computes derivative acquired values (W?). From the values of the original results (W) and the values of derivatives (W?), The amplitude (A? x) (Ax). Appointed? frequency vibrates? (f) which is directly proportional to the amplitude of the signal derivative (A x x) and inversely proportional to the double product of the constant? and signal amplitude (Ax). The obtained result looks like in a result block (BW), preferably on the screen of the computer device (K).

The solution according to the invention uses an algorithm that allows to determine the main harmonic component for a given waveform of any physical or mathematical quantity. The principle of the method is based on on comparing the signal amplitude with the amplitude derivative of a signal. For a harmonic signal one can write? equation of motion in the form: Image available on "Original document" where: A - signal amplitude, f - frequency signal, ? - phase shift.

Then a derivative? signal with respect to time can be presented in the following form: Image available on "Original document" In this case, the amplitude of the signal derivative is equal to: - 2Af. You see? so that the frequency of of the primary signal affects the amplitude derivative of a signal. So comparing with each other? the amplitude of the signal and its derivative with respect to time can be determined its frequency. Yes? dependency you can present with the following equation: Image available on "Original document" where: f - searched frequency, AND? - amplitude of the signal derivative, Ax - signal amplitude.

The method of determining both amplitudes is optional. In practice, you can apply for this purpose the maximum worth it ?? absolute the signal and its derivative, respectively. The presented algorithm is characterized by numerical simplification, which will be discussed in more detail below.

Fig. 1 - Fig. 6 shows the waveforms of the analyzed signal x (t) generated for a frequency of 80 Hz, corresponding to different numbers of samples, as well as their frequency domain spectra. ci calculated from the Fourier transform.

Fig. 2 shows the frequency spectrum of the signal of Fig. 1. In the frequency domain, distinct bands, one of which corresponds to the main harmonic component, and the other is its mirror image resulting from the duplication of the main component with respect to the sampling frequency (spectral diagram g The power is supposed to be symmetrical). A band on the basis of which you can read the task? frequency signal, how should it be? As expected, it is slightly below the value of 100 Hz, which corresponds to the set frequency of 80 Hz. However, a characteristic blurring of the band is visible, which makes it impossible to read the frequency accurately. It's worth ?? the maximum occurs exactly at the value of 97 Hz, which means an error in measuring the frequency within 17 Hz.

Meanwhile, for the same signal analyzed by means of proposed algorithm, calculated value ?? frequency was 79 Hz. This causes a measurement error within 1 Hz.

This phenomenon is even more interesting when we reduce the numbers? half of analyzed samples. The course of such a signal was shown in Fig. 3. As you can see, in the analyzed area there are fragment of the harmonic waveform containing little more than one period of twitch ?. This is a situation for ?? difficult to analyze frequency by means of Fourier transform.

Widmow? density calculated power? for this signal using? the Fourier transform is shown in Fig. 4. The resulting bands give si? much more unambiguous, however, the maximum fringe corresponding to the main harmonic component falls at the frequency of 67 Hz. This means an error of 13 Hz in relation to the set frequency of 80 Hz in the signal.

Frequency The main harmonic component calculated on the basis of the presented method is again 79 Hz, which means an error within 1 Hz.

Fig. 5 shows the signal harmonic with a frequency of 80 Hz, represented this time by 8 samples. This means that the analyzed area does not include even a single period trembles? described by a signal. Spectral Density power for such a signal is shown in Fig. 6, the main harmonic component read from the diagram is 143 Hz, which causes an error of 63 Hz (i.e. a relative error of almost 80%) . Such a big mistake should come as no surprise, considering the very small numbers? signal samples that reduce the accuracy of face? for help? Fourier transform.

For the same signal analyzed with? of the presented algorithm read value ?? the frequency of the main harmonic component was 78 Hz, which means an error within 2 Hz. This example illustrates the aforementioned fact, that the presented calculation method at low relative frequencies is characterized by very little ?? sensitivity? the accuracy of the calculations on numbers? samples in signal as long as they include? they are at least three-quarters of the period of the main harmonic.

The simulations of the use of the two computational methods compared to the determination of the main harmonic component were carried out for different frequencies set in the signal. In the following Figs. 7 - 9, the values of the relative error in the frequency domain are shown. The continuous line corresponds to the results of the Fourier transformation, and the dashed line corresponds to the results of the presented method. Fig. 7 shows the results for the number of samples being 32, Fig. 8 for the number of samples equal to 16, and Fig. 9 for the number of samples being 8.

As it results from the presented graphs, in the lower frequency ranges the values of the relative error are smaller in the case of the presented method, but each time there is a certain frequency the limit, above which the Fourier analysis gives the best results. It is worth noting, however, that the w? Frequency? border increases? with decreasing? the number of samples. This is due to the fact which would? already? emphasized in this article, according to which the presented method has little effect on the reduction of the number of signal samples. This means that it is the most justified in the case of a small number of samples.

There is still the problem of the sensitivity of the presented method to "contamination" of the analyzed signal by means of other harmonic components. As mentioned above, the presented method works? preferably in a situation where additional components do not exceed? ten percent of the main component. This is the case when the signal? comes from one, dominant source - for example, from an internal combustion engine treated as a whole.

In Fig. 10, the relationship The relative error of the methods considered in the frequency domain of the main signal disturbed by other frequency components at the level of forty percent of the main signal. This means very unfavorable conditions for the presented method.

How can you see? in the above case, the range of frequencies at which the proposed algorithm causes a smaller error than Fourier transform, falls within in a small range (40 - 130 Hz).

So you can present? usefulness of the presented method (compared to the analysis by means of the Fourier transform) in the two-dimensional domain: the frequency of the analyzed signal and the ratio of the amplitudes of the additional components to the amplitude of the main signal component. Yes? dependency is shown in Fig. 11. The bright area corresponds to the situation in which the presented method gives the results more precisely than Fourier transform.

As can be seen, for an amplitude ratio below 10%, the range of usable frequencies extends to about 200 Hz, but as the ratio increases, the frequency range decreases to 120 Hz. It provides a certain framework for the applicability of the presented method. However, it should be emphasized that in the case of reducing the number of samples of the analyzed signal, the applicability of method will be increases as a result of the deterioration of the properties of Fourier analysis. The above considerations have been presented for the number of samples equal to 32.

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Claims (1)

The method of measuring the frequency of vibrations, characterized by the fact that sensor (Cz) is performed measuring the course of variability of a given physical value, preferably vibration acceleration from the reference value which is converted to on signal? digital carrier of the obtained results (W), signal this one passes on to the memory of a computer device (K), to the computation block (BO) where is this signal? the carrier of the obtained results (W) is separated by parallel to the result channels (KW1, KW2), then from the result channel signal (KW1) using a mathematical algorithm computes derivative of the obtained values (W?), then the values of the primary results (W) and the values of derivatives (W?) are amplitude (A? x) (Ax), then frequency vibrates? (f) which is directly proportional to the amplitude of the signal derivative (A x x) and inversely proportional to the double product of the constant? and signal amplitude (Ax), the obtained result is in a result block (BW), preferably on the screen of the computer device (K). The method according to p. According to claim 1, characterized in that the computation block is (BO) is communicated? signal? as a result carrier (W) in real time or signal? historical stored in the memory (P) of a computer device (K). The method according to p. A sensor according to claim 1, characterized in that the external sensor (Cz) is a sensor of any physical size, in particular is a strain gauge or a vibration sensor. waves caused? acoustic. . . Don't show this again