CN115060355A - Harmonic oscillator quality factor measuring method based on linear frequency modulation pulse - Google Patents

Harmonic oscillator quality factor measuring method based on linear frequency modulation pulse Download PDF

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CN115060355A
CN115060355A CN202210380357.1A CN202210380357A CN115060355A CN 115060355 A CN115060355 A CN 115060355A CN 202210380357 A CN202210380357 A CN 202210380357A CN 115060355 A CN115060355 A CN 115060355A
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李宏生
刘蓉
丁徐锴
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Abstract

The invention provides a harmonic oscillator quality factor measuring method based on a linear frequency modulation pulse signal
Figure DEST_PATH_IMAGE002
(ii) a For response signal
Figure 860058DEST_PATH_IMAGE002
Sampling, FFT transforming, modulus taking and normalizing to obtain frequency spectrum
Figure DEST_PATH_IMAGE004
(ii) a Cut-select swept range spectrum
Figure DEST_PATH_IMAGE006
Calculating to obtain the estimated value of the vibration frequency
Figure DEST_PATH_IMAGE008
(ii) a Establishing a Lorentz curve model and a frequency range of the first Lorentz fitting
Figure DEST_PATH_IMAGE010
Q value range 1
Figure DEST_PATH_IMAGE012
Q
Figure 59089DEST_PATH_IMAGE012
M，Performing a first estimation of the figure of merit; combining the first estimate
Figure DEST_PATH_IMAGE014
In frequency sweep universe
Figure DEST_PATH_IMAGE016
Range of Q value
Figure DEST_PATH_IMAGE018
And carrying out second Lorentz fitting to obtain a final quality factor estimation value. The method not only improves the larger error of the half-power bandwidth method in the low signal-to-noise ratio environment, but also saves the operation time through the two-step fitting process, and particularly has obvious advantages for some harmonic oscillators with high Q values.

Description

Harmonic oscillator quality factor measuring method based on linear frequency modulation pulse
Technical Field
The invention relates to the field of resonant device parameter measurement, in particular to a harmonic oscillator quality factor measuring method based on linear frequency modulation pulse.
Background
The quality factor is an important parameter of the vibration characteristic of the resonant device, and plays an important role in drive control and error mechanism analysis. The quality factor measuring method is mainly divided into a time domain method and a frequency domain method. The time domain method is based on the amplitude attenuation characteristic during free oscillation, and is calculated by utilizing the attenuation degree of the oscillation amplitude in specific time and the corresponding relation between the attenuation degree and the Q value, the peak value or the amplitude envelope of transient response needs to be detected, and the method is relatively complex. The frequency domain method is commonly used, and is generally calculated by using a resonance frequency and a pass band width based on an amplitude-frequency characteristic curve, and is called a half-power bandwidth method. However, when the signal-to-noise ratio is low, the reliability of the half-power bandwidth method is low, and the error is large.
Disclosure of Invention
In order to solve the problems, the invention discloses a harmonic oscillator quality factor measuring method based on linear frequency modulation pulses, which aims to solve the problem of large quality factor measuring error under the condition of low signal-to-noise ratio.
In order to achieve the above purpose, the invention adopts the following scheme:
a harmonic oscillator quality factor measuring method based on linear frequency modulation pulse comprises the following steps:
step 1: carrying out frequency sweeping excitation on the harmonic oscillator by using a chirp signal to obtain a response signal s (t);
step 2: sampling, FFT (fast Fourier transform), modulus taking and normalization are carried out on the response signal S (t) to obtain a frequency spectrum | S' (n) |; interception and selection sweep range spectrum | S 1 ' (n) | calculation obtains the estimated value of the vibration frequency
Figure BDA0003592653200000021
And step 3: and establishing a Lorentz curve model, sequentially carrying out Lorentz fitting twice aiming at different frequency ranges, and combining the resonant frequency value obtained in the previous step to obtain the quality factor.
The step 3 comprises the following steps:
step 3.1: establishing Lorentz curve model
Figure BDA0003592653200000022
Figure BDA0003592653200000023
Is the estimated resonant frequency, Q is the quality factor, and the Q max is set to M. If Q ═ m, drawing L (f) non-calculation Q＝m And normalizing to obtain L' (f) dichotomy Q＝m ；
Step 3.2: first Lorentzian fitting frequency range
Figure BDA0003592653200000024
The Q value range is more than or equal to 1 and less than or equal to M. Subtracting the amplitude of each data point in the actual frequency range from the amplitude of the frequency point corresponding to the fitting curve point by point and accumulating to obtain a residual error (m);
step 3.3: index residual error sequence error (i)) The point with the smallest value, the sequence number is denoted index0, and the figure of merit of the first estimation is obtained
Figure BDA0003592653200000025
Step 3.4: the second Lorentz fitting f range is in the whole sweep frequency domain interval f 1 ≤f≤f 2 Selecting the range of Q value as
Figure BDA0003592653200000026
Repeating the step 3.3 to obtain a residual error sequence error (i);
step 3.5: the point with the minimum value in the index residual error sequence error (i) is marked as index1 to obtain the final estimation value of the quality factor
Figure BDA0003592653200000027
The invention has the beneficial effects that: the method not only improves the larger error of the half-power bandwidth method in the low signal-to-noise ratio environment, but also saves the operation time through the two-step fitting process, and particularly has obvious advantages for some harmonic oscillators with high Q values.
Drawings
Fig. 1 is a flowchart of a harmonic oscillator quality factor measurement method based on chirp pulses provided in the present invention;
FIG. 2 is a comparison of simulation results of the half-power bandwidth method and the method of the present invention with respect to error.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention. It should be noted that the terms "front," "back," "left," "right," "upper" and "lower" used in the following description refer to directions in the drawings, and the terms "inner" and "outer" refer to directions toward and away from, respectively, the geometric center of a particular component.
As shown in fig. 1-2, the method for measuring the quality factor of a harmonic oscillator based on chirp of this embodiment sets chirpParameters of the signal: starting frequency f 1 End frequency f 2 Sweep frequency time T, signal amplitude A, generating chirp signal x (T):
Figure BDA0003592653200000031
wherein
Figure BDA0003592653200000032
Carrying out frequency sweeping excitation on the harmonic oscillator by using a chirp signal to obtain a response signal s (t);
by the sampling rate f s Sampling the response signal S (T), then performing FFT (fast Fourier transform) and modulus to obtain a frequency spectrum | S (N) |, the length is N, the resolution ratio delta f of the frequency spectrum is 1/T, and normalizing the frequency spectrum to obtain | S' (N) |.
|S(n)|＝|X(n)|·|G(n)| (2)
Wherein | x (n) | is the frequency spectrum of chirp in the frequency domain; | G (n) | is the mode of harmonic oscillator amplitude-frequency characteristics; n is 1, 2, …, N;
the sweep frequency range in interception | S' (n) | is f 1 ≤f≤f 2 Inner spectrum | S 1 ′(n)|，f 1 Corresponding spectral line number N 1 、f 2 Corresponding spectral line number N 2 I.e. | S 1 ′(n)|＝|S′(n)|，N 1 ≤n≤N 2 ：
Figure BDA0003592653200000041
To | S 1 ' (n) | is subjected to spectral peak indexing, and the serial number of a spectral line corresponding to a spectral peak is k 0 Peak amplitude of | S 1 ′(k 0 ) Obtaining an estimate of the resonant frequency
Figure BDA0003592653200000042
Establishing a Lorentz curve model L (f):
Figure BDA0003592653200000043
Figure BDA0003592653200000044
is the estimated resonant frequency, let the Q max be M.
If Q ═ m, drawing L (f) & gtnon-calculation Q＝m Is normalized to obtain L' (f) luminance Q＝m ；
The first Lorentzian fitting frequency f is in the range
Figure BDA0003592653200000045
The Q value range is more than or equal to 1 and less than or equal to M.
The frequency spectrum sequence corresponding to the frequency range is that the amplitude of each data point in the actual frequency range and the frequency point corresponding to the fitting curve are subtracted point by point and accumulated to obtain a residual error (m):
Figure BDA0003592653200000046
the point with the smallest value in the index residual error sequence error (i), with the sequence number marked as index0, obtains the first estimated quality factor value
Figure BDA0003592653200000047
The second Lorentz fitting f range is in the whole sweep frequency domain interval f 1 ≤f≤f 2 Selecting the range of Q value as
Figure BDA0003592653200000051
Repeating the step 3.3 to obtain a residual error sequence error (i):
Figure BDA0003592653200000052
the point with the minimum value in the index residual error sequence error (i) is marked as index1 to obtain the final estimation value of the quality factor
Figure BDA0003592653200000053
Because the half-power bandwidth method only utilizes three points of the response signal frequency spectrum to calculate, and Lorentz fitting utilizes all the points in the effective frequency range, the error can be reduced for the signal with low signal-to-noise ratio; compared with the Lorentz fitting only once, the two-step fitting can save the operation time, especially for some harmonic oscillators with high Q values.
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features.

Claims (4)

1. A harmonic oscillator quality factor measuring method based on chirp is characterized by comprising the following steps:
step 1: carrying out frequency sweeping excitation on the harmonic oscillator by using a chirp signal to obtain a response signal s (t);
step 2: sampling, FFT (fast Fourier transform), modulus taking and normalization are carried out on the response signal S (t) to obtain a frequency spectrum | S' (n) |; interception and selection sweep range spectrum | S 1 ' (n) | calculation obtains the estimated value of the vibration frequency
Figure FDA0003592653190000011
And step 3: establishing a Lorentz curve model, and obtaining a frequency range of the first Lorentz fitting by using a half-power bandwidth method
Figure FDA0003592653190000012
Q is more than or equal to 1 and less than or equal to M, and the quality factor is estimated for the first time; combining the first estimate
Figure FDA0003592653190000013
At swept frequency universe f 1 ≤f≤f 2 ，
Figure FDA0003592653190000014
And carrying out second Lorentz fitting to obtain a final quality factor estimation value.
2. The method of claim 1, wherein the harmonic oscillator quality factor is measured based on a chirp signal,
setting parameters of the chirp signals in the step 1: starting frequency f 1 End frequency f 2 Sweep frequency time T, signal amplitude A, generating chirp signal x (T):
Figure FDA0003592653190000015
wherein
Figure FDA0003592653190000016
And (5) carrying out frequency sweeping excitation on the harmonic oscillator by using a chirp signal to obtain a response signal s (t).
3. The method for measuring the quality factor of the harmonic oscillator based on the chirp according to claim 1, wherein the step 2 is to use a sampling rate f s Sampling the response signal S (T), then performing FFT (fast Fourier transform) and modulus to obtain a frequency spectrum | S (N) |, the length is N, the resolution ratio delta f of the frequency spectrum is 1/T, and normalizing the frequency spectrum to obtain | S' (N) |.
|S(n)|＝|X(n)|·|G(n)| (2)
Where | x (n) | is the frequency spectrum of chirp in the frequency domain; | G (n) | is the mode of harmonic oscillator amplitude-frequency characteristics; n is 1, 2, …, N;
the sweep frequency range in the interception and selection | S' (n) | is f 1 ≤f≤f 2 Inner frequency spectrum | S 1 ′(n)|，f 1 Corresponding spectral line number N 1 、f 2 Corresponding spectral line number N 2 I.e. | S 1 ′(n)|＝|S′(n)|，N 1 ≤n≤N 2 ：
Figure FDA0003592653190000021
To | S 1 ' (n) | is subjected to spectral peak indexing, and the serial number of a spectral line corresponding to a spectral peak is k 0 Peak amplitude of | S 1 ′(k 0 ) Obtaining an estimate of the resonant frequency
Figure FDA0003592653190000022
4. The method for measuring the quality factor of the harmonic oscillator based on the chirp according to claim 1, wherein the step 3 comprises:
step 3.1: establishing Lorentz curve model
Figure FDA0003592653190000023
Figure FDA0003592653190000024
Is the estimated resonant frequency, Q is the quality factor, and the maximum value of Q is set to M; if Q ═ m, drawing L (f) & gtnon-calculation Q＝m And normalizing to obtain L' (f) dichotomy Q＝m ；
Step 3.2: the first Lorentzian fitting frequency f is in the range
Figure FDA0003592653190000025
The Q value range is more than or equal to 1 and less than or equal to M. Subtracting the amplitude of each data point in the actual frequency range from the amplitude of the frequency point corresponding to the fitting curve point by point and accumulating to obtain a residual error (m);
step 3.4: the point with the smallest value in the index residual error sequence error (i), with the sequence number marked as index0, obtains the first estimated quality factor value
Figure FDA0003592653190000026
Step 3.5: the second Lorentz fitting f range is in the whole sweep frequency domain interval, and the Q value range is selected as
Figure FDA0003592653190000027
Repeating the step 3.3 to obtain a residual error sequence error (i);
step 3.6: the point with the minimum value in the index residual error sequence error (i) is marked as index1 to obtain the final estimation value of the quality factor
Figure FDA0003592653190000031
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