CN115060355B - Harmonic oscillator quality factor measurement method based on linear frequency modulation pulse - Google Patents

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

Info

Publication number
CN115060355B
CN115060355B CN202210380357.1A CN202210380357A CN115060355B CN 115060355 B CN115060355 B CN 115060355B CN 202210380357 A CN202210380357 A CN 202210380357A CN 115060355 B CN115060355 B CN 115060355B
Authority
CN
China
Prior art keywords
frequency
quality factor
spectrum
lorentz
value
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202210380357.1A
Other languages
Chinese (zh)
Other versions
CN115060355A (en
Inventor
李宏生
刘蓉
丁徐锴
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Southeast University
Original Assignee
Southeast University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Southeast University filed Critical Southeast University
Priority to CN202210380357.1A priority Critical patent/CN115060355B/en
Publication of CN115060355A publication Critical patent/CN115060355A/en
Application granted granted Critical
Publication of CN115060355B publication Critical patent/CN115060355B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H13/00—Measuring resonant frequency
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Data Mining & Analysis (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Evolutionary Biology (AREA)
  • Operations Research (AREA)
  • Probability & Statistics with Applications (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

The invention provides a method for measuring quality factor of harmonic oscillator based on linear frequency modulation pulse signal, which comprises the steps of firstly using the linear frequency modulation pulse signal to carry out sweep frequency excitation on the harmonic oscillator to obtain a response signalThe method comprises the steps of carrying out a first treatment on the surface of the Responsive to a response signalSampling, FFT, modulo, normalizing to obtain frequency spectrumThe method comprises the steps of carrying out a first treatment on the surface of the Frequency spectrum of frequency sweeping range is cut offCalculating to obtain the estimated value of the vibration frequencyThe method comprises the steps of carrying out a first treatment on the surface of the Establishing a Lorentz curve model, and fitting the frequency range of the first LorentzQ value range 1 Q M，Performing first estimation on the quality factor; combining the first estimateIn the whole domain of sweep frequencyQ value rangeAnd (5) performing second Lorentz fitting to obtain a final quality factor estimated value. The method not only improves larger errors of the half-power bandwidth method in a low signal-to-noise ratio environment, but also saves operation time through a two-step fitting process, and particularly has obvious advantages for some high-Q-value resonators.

Description

Harmonic oscillator quality factor measurement method based on linear frequency modulation pulse
Technical Field
The invention relates to the field of parameter measurement of resonant devices, in particular to a harmonic oscillator quality factor measurement method based on linear frequency modulation pulses.
Background
The quality factor is an important parameter of the vibration characteristics of the resonant device, and plays an important role in driving control and error mechanism analysis. The quality factor measurement 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 a specific time and the corresponding relation between the oscillation amplitude and the Q value, and the peak value or the amplitude envelope of the transient response needs to be detected, so that the time domain method is relatively complex. The frequency domain method is more commonly used, and is generally calculated based on an amplitude-frequency characteristic curve by using a resonance frequency and a passband bandwidth, 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 measurement method based on linear frequency modulation pulses, which aims to solve the problem of larger quality factor measurement error under the condition of low signal to noise ratio.
In order to achieve the above object, the present invention adopts the following scheme:
a harmonic oscillator quality factor measuring method based on linear frequency modulation pulse comprises the following steps:
step 1: using chirp signals to carry out sweep frequency excitation on the harmonic oscillator to obtain response signals s (t);
step 2: sampling, FFT (fast Fourier transform), modulo, and normalizing the response signal S (t) to obtain a frequency spectrum |S' (n) |; cut off frequency spectrum |S of sweep frequency range 1 'n' is calculated to obtain the estimated value of the vibration frequency
Step 3: and (3) establishing a Lorentz curve model, successively carrying out Lorentz fitting twice according to different frequency ranges, and obtaining a quality factor by combining the resonance frequency values obtained in the previous step.
The step 3 comprises the following steps:
step 3.1: establishing Lorentz curve model Is the estimated resonant frequency, Q is the quality factor, and the Q maximum is set to M. If q=m, draw L (f) | Q＝m And normalized to obtain L' (f) | Q＝m ；
Step 3.2: first Lorentz fitting frequency rangeQ value is more than or equal to 1 and less than or equal to M. The frequency corresponding to each data point in the actual frequency range and the fitting curve is calculatedThe magnitudes of the points are subjected to point-by-point difference and accumulated to obtain residual error (m);
step 3.3: indexing the point with the minimum value in the residual error sequence error (i), and marking the sequence number as index0 to obtain the quality factor value estimated for the first time
Step 3.4: the second Lorentz fit f ranges over the whole sweep domain interval f 1 ≤f≤f 2 Selecting the Q value range asRepeating the step 3.3 to obtain a residual sequence error (i);
step 3.5: indexing the point with the minimum value in the residual error sequence error (i), and marking the sequence number as index1 to obtain the final estimated value of the quality factor
The invention has the beneficial effects that: the method improves larger errors of the half-power bandwidth method in a low signal-to-noise ratio environment, saves operation time through a two-step fitting process, and has obvious advantages especially for some high-Q-value resonators.
Drawings
FIG. 1 is a flow chart of a method for measuring the quality factor of a harmonic oscillator based on a chirp pulse;
FIG. 2 is a comparison of the relative error between the simulation results of the half-power bandwidth method and the method of the present invention.
Detailed Description
The present invention is further illustrated in the following drawings and detailed description, which are to be understood as being merely illustrative of the invention and not limiting the scope of the invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to directions in the drawings, and the words "inner" and "outer" refer to directions toward or away from, respectively, the geometric center of a particular component.
As shown in fig. 1-2, in the method for measuring quality factor of harmonic oscillator based on chirp, parameters of the chirp signal are set: initial frequency f 1 Termination frequency f 2 Generating a chirp signal x (T):
wherein the method comprises the steps of
Sweeping excitation is carried out on the harmonic oscillator by using a chirp signal, so as to obtain a response signal s (t);
by sampling rate f s The response signal S (T) is sampled, then the FFT is performed and modulo is performed to obtain a frequency spectrum |S (N) |, the length is N, the resolution Deltaf=1/T of the frequency spectrum is normalized to obtain |S' (N) |.
|S(n)|＝|X(n)|·|G(n)| (2)
Where |x (n) | is the spectrum of chirp in the frequency domain; the I G (n) I is a mode of amplitude-frequency characteristics of the harmonic oscillator; n=1, 2, …, N;
cut off the sweep frequency range in |S' (n) | to be f 1 ≤f≤f 2 Spectrum |S in 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 ：
For |S 1 ' (n) | carrying out spectrum peak index, wherein the spectral line serial number corresponding to the spectrum peak is k 0 Spectral peak amplitude is |S 1 ′(k 0 ) I, obtain an estimate of the resonant frequency
Establishing a Lorentzian curve model L (f):
is the estimated resonant frequency, and the Q maximum is set to M.
If q=m, draw L (f) | Q＝m And normalized to obtain L' (f) | Q＝m ；
The first Lorentz fitting frequency f ranges fromQ value is more than or equal to 1 and less than or equal to M.
The frequency spectrum sequence corresponding to the frequency range is to make the difference between each data point in the actual frequency range and the amplitude of the frequency point corresponding to the fitting curve point by point and accumulate the difference to obtain a residual error (m):
indexing the point with the minimum value in the residual error sequence error (i), and marking the sequence number as index0 to obtain the quality factor value estimated for the first time
The second Lorentz fit f ranges over the whole sweep domain interval f 1 ≤f≤f 2 Selecting the Q value range asRepeating the step 3.3 to obtain a residual sequence error (i):
indexing the point with the minimum value in the residual error sequence error (i), and marking the sequence number as index1 to obtain the final estimated value of the quality factor
The half-power bandwidth method only uses three points of the response signal spectrum for calculation, and Lorentz fitting uses all points in the effective frequency range, so that errors can be reduced for signals with low signal-to-noise ratio; compared with the method for performing Lorentz fitting only once, the two-step fitting can save more operation time, especially for some high-Q-value resonators.
The technical means disclosed by the scheme of the invention is not limited to the technical means disclosed by the embodiment, and also comprises the technical scheme formed by any combination of the technical features.

Claims (1)

1. A method for measuring a quality factor of a harmonic oscillator based on a chirp pulse, the method comprising the steps of:
step 1: using chirp signals to carry out sweep frequency excitation on the harmonic oscillator to obtain response signals s (t);
step 2: sampling, FFT (fast Fourier transform), modulo, and normalizing the response signal S (t) to obtain a frequency spectrum |S' (n) |; cut off frequency spectrum |S of sweep frequency range 1 'n' is calculated to obtain the estimated value of the vibration frequency
Step 3: establishing a Lorentz curve model, and obtaining a frequency range of a first Lorentz fitting by using a half-power bandwidth methodPerforming first estimation on the quality factor; combining the first estimateIn the sweep frequency domain f 1 ≤f≤f 2 ，/>Performing second Lorentz fitting to obtain a final quality factor estimated value; setting parameters of the chirp signal in the step 1: initial frequency f 1 Termination frequency f 2 Generating a chirp signal x (T):
wherein the method comprises the steps ofSweeping excitation is carried out on the harmonic oscillator by using a chirp signal, so as to obtain a response signal s (t); the step 2: by sampling rate f s Sampling a response signal S (T), performing FFT (fast Fourier transform) and taking a modulus to obtain a frequency spectrum |S (N) |, wherein the length is N, the resolution Deltaf=1/T of the frequency spectrum, and normalizing the frequency spectrum to obtain |S' (N) |;
|S(n)|＝|X(n)|·|G(n)| (2)
where |x (n) | is the spectrum of chirp in the frequency domain; the I G (n) I is a mode of amplitude-frequency characteristics of the harmonic oscillator; n=1, 2, …, N;
cut off the sweep frequency range in |S' (n) | to be f 1 ≤f≤f 2 Spectrum |S in 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 ：
For |S 1 ' (n) | carrying out spectrum peak index, wherein the spectral line serial number corresponding to the spectrum peak is k 0 Spectral peak amplitude is |S 1 ′(k 0 ) I, obtain an estimate of the resonant frequencyThe step 3 comprises the following steps:
step 3.1:
establishing Lorentz curve model Is the estimated resonant frequency, Q is the quality factor, and the maximum value of Q is set to M; if q=m, draw L (f) | Q＝m And normalized to obtain L' (f) | Q＝m ；
Step 3.2: the first Lorentz fitting frequency f ranges fromQ is more than or equal to 1 and less than or equal to M; the amplitude of each data point in the actual frequency range and the frequency point corresponding to the fitting curve are subjected to point-by-point difference and accumulated to obtain a residual sequence error (m);
step 3.3: indexing the point with the minimum value in the residual error sequence error (m), and marking the sequence number as index0 to obtain the quality factor value estimated for the first time
Step 3.4: the second Lorentz fitting f range is in the whole sweep frequency domain interval, and the Q value range is selected asRepeating the step 3.3 to obtain a residual sequence error (i); error (i):
step 3.5: indexing the point with the minimum value in the residual error sequence error (i), and marking the sequence number as index1 to obtain the final estimated value of the quality factor
CN202210380357.1A 2022-04-12 2022-04-12 Harmonic oscillator quality factor measurement method based on linear frequency modulation pulse Active CN115060355B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210380357.1A CN115060355B (en) 2022-04-12 2022-04-12 Harmonic oscillator quality factor measurement method based on linear frequency modulation pulse

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210380357.1A CN115060355B (en) 2022-04-12 2022-04-12 Harmonic oscillator quality factor measurement method based on linear frequency modulation pulse

Publications (2)

Publication Number Publication Date
CN115060355A CN115060355A (en) 2022-09-16
CN115060355B true CN115060355B (en) 2024-03-26

Family

ID=83196876

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210380357.1A Active CN115060355B (en) 2022-04-12 2022-04-12 Harmonic oscillator quality factor measurement method based on linear frequency modulation pulse

Country Status (1)

Country Link
CN (1) CN115060355B (en)

Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5257544A (en) * 1992-01-22 1993-11-02 The Board Of Trustees Of The Leland Stanford Junior University Resonant frequency method for bearing ball inspection
CN202562949U (en) * 2012-04-27 2012-11-28 南京信息工程大学 Resonant type micro-accelerometer based on static rigidity
EP2894521A1 (en) * 2014-01-13 2015-07-15 Ecole Polytechnique Federale de Lausanne (EPFL) Isotropic harmonic oscillator and associated time base without escapement or simplified escapement
CN105258786A (en) * 2015-11-03 2016-01-20 中国科学院半导体研究所 Rapid measurement of resonant frequency and quality factor of high-frequency harmonic oscillator
CN108507556A (en) * 2018-03-19 2018-09-07 中国人民解放军国防科技大学 Method and device for correcting and adjusting non-uniform quality factors of gyro harmonic oscillators with cylindrical shells
CN109490852A (en) * 2017-09-10 2019-03-19 北京遥感设备研究所 A kind of chirp pulse signal chirp rate polarity determination method
CN109490853A (en) * 2017-09-10 2019-03-19 北京遥感设备研究所 Spectral line value determines method at a kind of chirp pulse signal centre frequency
CN110823530A (en) * 2019-11-13 2020-02-21 南京大学 Method for obtaining quality factor of micro-resonant cavity
CN111272193A (en) * 2020-02-17 2020-06-12 东南大学 MEMS gyroscope online frequency difference identification method based on noise power spectrum estimation
CN112559956A (en) * 2020-12-23 2021-03-26 江苏睿科大器机器人有限公司 Wavelet threshold adaptive shrinkage method, system, electronic device and storage medium
CN113218547A (en) * 2020-02-06 2021-08-06 天津大学 Structure of high-Q perforated flexible micro-ring resonant cavity for double sensing

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6892155B2 (en) * 2002-11-19 2005-05-10 Agilent Technologies, Inc. Method for the rapid estimation of figures of merit for multiple devices based on nonlinear modeling
JP3920233B2 (en) * 2003-02-27 2007-05-30 ティーオーエー株式会社 Dip filter frequency characteristics determination method
US8676543B2 (en) * 2009-06-23 2014-03-18 Exxonmobil Research And Engineering Company Determining the resonance parameters for mechanical oscillators
US9335203B2 (en) * 2013-08-28 2016-05-10 Robert Bosch Gmbh MEMS component

Patent Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5257544A (en) * 1992-01-22 1993-11-02 The Board Of Trustees Of The Leland Stanford Junior University Resonant frequency method for bearing ball inspection
CN202562949U (en) * 2012-04-27 2012-11-28 南京信息工程大学 Resonant type micro-accelerometer based on static rigidity
EP2894521A1 (en) * 2014-01-13 2015-07-15 Ecole Polytechnique Federale de Lausanne (EPFL) Isotropic harmonic oscillator and associated time base without escapement or simplified escapement
CN105258786A (en) * 2015-11-03 2016-01-20 中国科学院半导体研究所 Rapid measurement of resonant frequency and quality factor of high-frequency harmonic oscillator
CN109490852A (en) * 2017-09-10 2019-03-19 北京遥感设备研究所 A kind of chirp pulse signal chirp rate polarity determination method
CN109490853A (en) * 2017-09-10 2019-03-19 北京遥感设备研究所 Spectral line value determines method at a kind of chirp pulse signal centre frequency
CN108507556A (en) * 2018-03-19 2018-09-07 中国人民解放军国防科技大学 Method and device for correcting and adjusting non-uniform quality factors of gyro harmonic oscillators with cylindrical shells
CN110823530A (en) * 2019-11-13 2020-02-21 南京大学 Method for obtaining quality factor of micro-resonant cavity
CN113218547A (en) * 2020-02-06 2021-08-06 天津大学 Structure of high-Q perforated flexible micro-ring resonant cavity for double sensing
CN111272193A (en) * 2020-02-17 2020-06-12 东南大学 MEMS gyroscope online frequency difference identification method based on noise power spectrum estimation
CN112559956A (en) * 2020-12-23 2021-03-26 江苏睿科大器机器人有限公司 Wavelet threshold adaptive shrinkage method, system, electronic device and storage medium

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
Cheng, HJ ; .Study on the Output of LD-Pumped Passively Q-switched Subnanosecond Microlasers.INTERNATIONAL SYMPOSIUM ON PHOTOELECTRONIC DETECTION AND IMAGING 2013: HIGH POWER LASERS AND APPLICATIONS.2013,全文. *
Electrical harmonic oscillator with MR damper and energy harvester operating as TMD: Experimental study;Bogdan Sapiński;Mechatronics;全文 *
Lin, TY ; .Analyzing OAM mode purity in optical fibers with CNN-based deep learning.CHINESE OPTICS LETTERS.2019,全文. *
一种高Q值硅微陀螺谐振频率快速锁定方法;吕正;测控技术;全文 *
光谱分辨率增强方法品质因子研究;高晓峰;光子学报;全文 *
基于多普勒测振的谐振子关键参数测量方法研究;马雪琳;中国优秀硕士学位论文全文数据库 (工程科技Ⅱ辑);全文 *

Also Published As

Publication number Publication date
CN115060355A (en) 2022-09-16

Similar Documents

Publication Publication Date Title
US6512788B1 (en) RF output spectrum measurement analyzer and method
US10998926B2 (en) Method for compensating gain flatness of transceiver
CN100495021C (en) Method for detecting inner defect of roller using ultrasonic wave
US7161511B2 (en) Linearization system and method
CN103200139B (en) A kind of ofdm signal bandwidth blind estimation
US10345365B2 (en) Reflectometry method and device for diagnosing cables in use
CN111693136B (en) Acoustic surface wave resonator frequency estimation algorithm adopting echo signal autocorrelation phase spectrum
CN102279396B (en) Broadband linearity frequency modulation pulse range finding method based on fractional order Fourier transformation
EP3586128B1 (en) Probing a structure of concrete by means of electromagnetic waves
CN113156206B (en) Time-frequency combined noise-containing signal parameter estimation new algorithm
JP5840868B2 (en) Frequency detection method and apparatus
CN109682492B (en) Frequency estimation method based on frequency domain Gaussian fitting
CN112162152B (en) Sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting
CN108398260B (en) Method for quickly evaluating instantaneous angular speed of gearbox based on mixed probability method
CN115060355B (en) Harmonic oscillator quality factor measurement method based on linear frequency modulation pulse
US7050487B2 (en) Method and circuit arrangement for determination of transmission parameters
CN104901907B (en) Data-aided steady signal-noise ratio estimation method is based under a kind of dynamic environment
CN109120562B (en) MFSK signal frequency estimation method based on spectrum accumulation matching
CN113406386B (en) Signal frequency accurate estimation method based on digital down-conversion
CN112444788B (en) Frequency estimation method of zero padding signal
JP4077092B2 (en) Doppler frequency measurement method and Doppler sonar
CN112468114B (en) FRI sampling system and method based on non-ideal sinc core
CN110208778B (en) Transducer broadband complex response measuring device and method based on logarithm variable window function
CN110687362A (en) Real-time phase noise testing method
CN100473175C (en) Method for determining envelope lines of modulation signals

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant