A method and device for calculating the quality factor of a hemispherical resonator

Abstract

The application discloses a kind of hemispherical resonator quality factor calculation method and device, method includes: after collecting hemispherical resonator resonance excitation revocation vibration attenuation signal is preprocessed, extract instantaneous total amplitude envelope sequence, then calculate the frequency crack of hemispherical resonator;According to the width of sliding window determined by frequency crack, extract the upper envelope of instantaneous total amplitude envelope sequence, and calculate envelope fluctuation modulation depth;If envelope fluctuation modulation depth is greater than 50%, logarithm is taken to the upper envelope, then carries out one-dimensional linear regression fitting, calculates Q value according to fitting parameter;If envelope fluctuation modulation depth is in the range of 5%-50%, apply a punitive shrink factor to the width of sliding window, and the Q value calculation method is the same as above;If envelope fluctuation modulation depth is 5%, the Q value is calculated by using time-domain full life cycle definite integral method, and the process is ended and exited.The present application can solve the technical problems existing in the prior art peak-seeking method, and realize accurate calculation of the quality factor of hemispherical resonator in various situations.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, specifically to a method and apparatus for calculating the quality factor of a hemispherical harmonic oscillator. Background Technology

[0002] The hemispherical resonator is the core sensing element of a hemispherical resonant gyroscope, and its quality factor (Q) is a key indicator of the resonator's low energy loss and high performance. A thorough understanding and accurate calculation of the hemispherical resonator's Q value is fundamental to the design and manufacture of high-precision inertial navigation systems.

[0003] In physics, the Q value is defined as: , For stored energy, This represents the energy loss per vibration cycle. A higher Q value (typically requiring millions or even tens of millions of units) means less external excitation energy is needed to maintain its standard n=2 bending vibration mode. A high Q value implies a longer free decay time. When there is a short-term power outage or strong interference, the harmonic oscillator can continue to vibrate for a longer period of time due to inertia, which greatly improves the system's anti-interference ability.

[0004] In dynamic measurement, based on the above definition, the classic calculation path is as follows: , It is the resonant frequency.

[0005] In actual testing, the free decay time of the acquired free decay signal is measured using digital signal processing. The process involves fitting the data and then calculating the Q-value. This means performing a Hilbert transform on the actual acquired signal to extract the envelope of the analytic signal. The main steps include: Signal acquisition: Acquire voltage or displacement signals during the free decay period. , Let t be the initial amplitude, and t be the instantaneous time. Angular frequency, This is the azimuth angle.

[0006] Constructing the analytic signal: obtained through Hilbert transform orthogonal imaginary part Constructing analytic signals .

[0007] Envelope Extraction: Calculate the modulus to obtain the instantaneous envelope of the signal. , Write a peak-finding algorithm to extract the peak maxima Xi corresponding to each time ti in the free decay waveform and form a set: (t1,X1),(t2,X2),…,(tn,Xn).

[0008] Using the exponential function Curve fitting is performed on these discrete peak points, and the fitted coefficient b is the decay rate, then the time constant. Then calculate the Q value.

[0009] The above method is intuitive and easy to understand. However, when the signal contains baseline drift or high-frequency glitches, peak finding is prone to errors, leading to calculation distortion. Furthermore, if the signal peaks are not obvious, the above method cannot be used for calculation. Summary of the Invention

[0010] To address the problems in the background technology, this invention proposes a method and apparatus for calculating the quality factor of a hemispherical harmonic oscillator. The C value is calculated using different methods based on the beat frequency strength of the acquired signal. This solves the technical problems of existing peak-finding methods, which are sensitive to noise, fail when the beat frequency signal is weak, and cannot adapt to the differences in signal morphology under different beat frequency intensities due to reliance on peak finding and single exponential fitting.

[0011] The present invention adopts the following technical solution: A method for calculating the quality factor of a hemispherical harmonic oscillator includes the following steps: S1: Acquire the vibration decay signal after the resonant excitation of the hemispherical harmonic oscillator is removed; S2: Preprocess the vibration attenuation signal to extract the instantaneous total amplitude envelope sequence; S3: Calculate the frequency split of the hemispherical harmonic oscillator based on the instantaneous total amplitude envelope sequence; S4: Determine the sliding window width based on the frequency splitting, then extract the upper envelope of the instantaneous total amplitude envelope sequence based on the sliding window width, and calculate the envelope wave modulation depth; S5: If the envelope wave modulation depth is greater than 50%, proceed to step S5.1; if the envelope wave modulation depth is within the range of 5%-50%, proceed to step S5.2; if the envelope wave modulation depth is less than 5%, proceed to step S5.3. S5.1: After taking the logarithm of the upper envelope, perform univariate linear regression fitting, calculate the quality factor of the hemispherical harmonic oscillator based on the obtained fitting parameters, and then terminate and exit. S5.2: Apply a penalty shrinkage factor to the sliding window width, re-extract the upper envelope of the instantaneous total amplitude envelope sequence with the shrunken sliding window width, take the logarithm of the upper envelope and perform univariate linear regression fitting, calculate the quality factor of the hemispherical harmonic oscillator based on the obtained fitting parameters, and then end and exit. S5.3: Calculate the quality factor of the hemispherical harmonic oscillator using the time-domain full-lifetime definite integral method, then end and exit.

[0012] Preferably, step S3 further includes: if frequency split = 0, proceed to step S5.3.

[0013] Preferably, step S1 specifically includes: applying resonant excitation in the working mode to the hemispherical harmonic oscillator to make it vibrate, removing the resonant excitation, and acquiring the vibration decay signal of the hemispherical harmonic oscillator.

[0014] Preferably, step S2 specifically includes: S2.1: Cascaded FIR downsampling filtering is used to reduce the sampling rate of the vibration attenuation signal to 20-30kHz; S2.2: Perform a short-time Fourier transform on the downsampled vibration attenuation signal to obtain its operating frequency range; S2.3: Within the operating frequency range, a robust regression algorithm is used to fit the absolute frequency drift rate. Then, the center frequency is calculated based on the absolute frequency drift rate compensation. Based on the center frequency, the downsampled vibration attenuation signal is subjected to multi-order Butterworth bandpass filtering. The filtering result is then subjected to Hilbert envelope transform to obtain the analytical signal. The original oscillation envelope sequence is obtained by taking the modulus of the analytical signal. The original oscillation envelope sequence is downsampled by an integer multiple to obtain the instantaneous total amplitude envelope sequence with a sampling rate of 8-10Hz.

[0015] Preferably, in step S2.3, based on the absolute frequency drift rate... The compensation calculation of the center frequency specifically includes: calculating the center frequency using the dynamic time-domain midpoint compensation method. , The starting frequency of the downsampled vibration attenuation signal, The absolute frequency drift rate, Sampling time.

[0016] Preferably, in step S4, determining the sliding window width based on frequency splitting specifically includes: sliding window width ,in It is a frequency crack.

[0017] Preferably, in step S4, calculating the envelope wave modulation depth specifically includes: Envelope wave modulation depth , , These represent the maximum and minimum envelope values ​​of the instantaneous total amplitude envelope sequence within the sliding window width, respectively.

[0018] Preferably, in steps S5.1 and S5.2, the upper envelope is... After taking the logarithm, a univariate linear regression is performed, specifically including: ,in, For the upper envelope, , , respectively, represent the slope and intercept of the univariate linear regression equation, where t is time; The quality factor of the hemispherical harmonic oscillator is calculated based on the obtained fitting parameters, specifically including: quality factor. .

[0019] Preferably, in step S5.2, the punitive contraction factor Width of the shrunk sliding window .

[0020] Preferably, in step S5.3, the quality factor of the hemispherical harmonic oscillator is calculated using the time-domain full-lifetime definite integral method, specifically including: Calculate the instantaneous energy curve of the filtered pure time-domain signal. Perform time-domain definite integral and time-weighted integral on the instantaneous energy curve within the effective lifetime. Calculate the quality factor of the hemispherical harmonic oscillator based on the time-domain definite integral and time-weighted integral.

[0021] Preferably, the instantaneous energy curve definite integral in the time domain Time-weighted integral The effective lifespan of the hemispherical harmonic oscillator is [0, T], and the quality factor of the hemispherical harmonic oscillator is... .

[0022] As a general inventive concept, the present invention also provides an apparatus for implementing the above-described method for calculating the quality factor of a hemispherical harmonic oscillator, comprising: The acquisition module is used to acquire the vibration decay signal after the resonant excitation of the hemispherical harmonic oscillator is removed; The preprocessing module is used to preprocess the vibration attenuation signal and extract the instantaneous total amplitude envelope sequence; the frequency splitting calculation module is used to calculate the frequency splitting of the hemispherical harmonic oscillator based on the instantaneous total amplitude envelope sequence. The envelope processing module is used to determine the sliding window width based on frequency splitting, extract the upper envelope of the instantaneous total amplitude envelope sequence based on the sliding window width, and calculate the envelope wave modulation depth. The quality factor calculation module is used to calculate the quality factor of the hemispherical harmonic oscillator when the envelope wave modulation depth is greater than 50%, by taking the logarithm of the upper envelope and performing univariate linear regression fitting, and then exiting based on the obtained fitting parameters; it is also used to apply a penalty contraction factor to the sliding window width when the envelope wave modulation depth is within the range of 5%-50%, re-extract the upper envelope of the instantaneous total amplitude envelope sequence with the contracted sliding window width, take the logarithm of the upper envelope and perform univariate linear regression fitting, and then calculate the quality factor of the hemispherical harmonic oscillator based on the obtained fitting parameters, and then exiting; it is also used to calculate the quality factor of the hemispherical harmonic oscillator using the time-domain full-lifetime definite integral method when the envelope wave modulation depth is 5%, and then exiting.

[0023] Compared with the prior art, the advantages of the present invention are as follows: The method for calculating the quality factor of a hemispherical harmonic oscillator in this invention abandons the traditional peak-finding method. It calculates the Q-value by extracting the upper envelope (strong / medium beat frequency) or definite integral (weak or no beat frequency), without relying on peak point detection, thus completely avoiding the errors of peak-finding and failure in weak beat frequency scenarios. For strong beat frequency signals, the monotonic upper envelope is first extracted, and then logarithmic linear regression is performed, solving the problem of easy collapse when directly taking the logarithm for non-monotonic envelopes. For medium beat frequency signals, a safety degradation defense and a penalty contraction factor are introduced, causing the sliding window to automatically contract as the beat frequency decreases, fundamentally eliminating the problem of excessive smoothing distortion. In the case of no beat frequency, the time-domain full-lifetime definite integral method is used, which allows zero-mean force random noise and instantaneous jitter to cancel each other out during the summation process, eliminating the influence of tail noise on the Q-value increase. Moreover, this calculation method is very lightweight and has an extremely high calculation speed. In summary, different methods are used to calculate the Q value based on the beat frequency strength of the acquired signal, which solves the technical problems of existing peak-finding methods, such as sensitivity to noise, failure when the beat frequency signal is weak, and inability to adapt to signal morphology differences under different beat frequency intensities, which are caused by reliance on peak finding and single exponential fitting. Attached Figure Description

[0024] To facilitate understanding of the invention, it will be described in more detail with reference to the specific embodiments shown in the accompanying drawings. These drawings depict only typical embodiments of the invention and should not be considered as limiting the scope of protection of the invention.

[0025] Figure 1 This is a schematic diagram of the processing of strong beat frequency signals in Embodiment 1 of the present invention.

[0026] Figure 2 This is a schematic diagram of the processing of medium-frequency signals in Embodiment 1 of the present invention.

[0027] Figure 3 This is a schematic diagram of the processing of beatless signals in Embodiment 1 of the present invention. Detailed Implementation

[0028] The embodiments of the present invention are described below with reference to the accompanying drawings to enable those skilled in the art to better understand and implement the present invention. However, the listed embodiments are not intended to limit the present invention. In the absence of conflict, the following embodiments and the technical features in the embodiments can be combined with each other, wherein the same components are indicated by the same reference numerals.

[0029] Example 1

[0030] This embodiment provides a method for calculating the quality factor of a hemispherical harmonic oscillator, including the following steps: S1: Acquire the vibration decay signal after the resonant excitation of the hemispherical harmonic oscillator is removed; In this embodiment, step S1 specifically includes: applying resonant excitation in the working mode to the hemispherical harmonic oscillator to make it vibrate, removing the resonant excitation, and acquiring the vibration decay signal of the hemispherical harmonic oscillator.

[0031] More specifically, the detailed execution process of step S1 is as follows: A hemispherical resonator is fixed to an excitation device, which provides excitation at the resonant frequency of the hemispherical resonator in its operating mode. After successful excitation and vibration, the excitation device is turned off, at which point the hemispherical resonator enters a vibration decay state until vibration stops. Using testing equipment such as a laser vibrometer, the detection point is aligned with the outer spherical surface of the hemispherical resonator near the lip, and the vibration signal at this location after vibration decay is measured. This vibration signal is the correlation data of vibration amplitude and time.

[0032] S2: Preprocess the vibration attenuation signal to extract the instantaneous total amplitude envelope sequence; In this embodiment, step S2 specifically includes: S2.1: Cascaded FIR downsampling filtering is used to reduce the sampling rate of the vibration attenuation signal to 20-30kHz; S2.2: Perform a short-time Fourier transform on the downsampled vibration attenuation signal to obtain its operating frequency range; S2.3: Within the operating frequency range, a robust regression algorithm is used to fit the absolute frequency drift rate. Then, the center frequency is calculated based on the absolute frequency drift rate compensation. Based on the center frequency, the downsampled vibration attenuation signal is subjected to multi-order Butterworth bandpass filtering. The filtering result is then subjected to Hilbert envelope transform to obtain the analytical signal. The original oscillation envelope sequence is obtained by taking the modulus of the analytical signal. The original oscillation envelope sequence is downsampled by an integer multiple to obtain the instantaneous total amplitude envelope sequence with a sampling rate of 8-10Hz.

[0033] The following is a detailed explanation of step S2: The frequency of a hemispherical resonator is typically in the thousands of Hz range, while the sampling rate of the original data can be as high as tens of thousands of Hz. To reduce subsequent computational load, the program employs a cascaded FIR sampling strategy: First, it checks if the current sampling rate is greater than the sum of twice the operating frequency and a 10% margin. If so, it performs an FIR downsampling by a factor of 2, halving the sampling rate. This process is repeated until the sampling rate is reduced to the 24kHz operating range. The FIR filter guarantees linear phase, meaning the signal has no phase distortion after downsampling. The cascaded strategy avoids the filter design difficulties caused by single large-scale sampling.

[0034] Since the collected data still contains a lot of noise, the signal is first cut into frame-by-frame segments using short-time Fourier transform (STFT) to analyze its approximate operating frequency range.

[0035] A dynamic tracking filter is formed by combining a robust regression algorithm. Because the frequency of the signal being searched is not fixed and drifts with factors such as temperature, the absolute frequency drift rate of the current file is first calculated. Absolute frequency drift rate The calculation process is as follows: Within the operating frequency range determined by the STFT, the actual peak frequency point is extracted for each frame of signal to form a discrete point series of "time-instantaneous frequency". Then, robust regression is performed on these points to fit the relationship between frequency f and time t, and the absolute frequency drift rate is calculated. Then, dynamic time-domain midpoint compensation is used to calculate the center frequency: , The starting frequency of the downsampled vibration attenuation signal, The absolute frequency drift rate, Sampling time.

[0036] Using the corrected center frequency Design a multi-order Butterworth bandpass filter with a single-side bandwidth of ±1Hz to filter out all out-of-band noise components. With a precise center frequency, a narrowband bandpass filter (center frequency) can be designed. With a bandwidth of only ±1Hz, the signal near the operating frequency is precisely extracted, and all out-of-band noise is eliminated. The filtered result is then subjected to a Hilbert envelope transform to obtain the analytic signal, and the original oscillation envelope is obtained by taking the modulus of the analytic signal. The Hilbert envelope transform is a standard method for extracting the envelope of an oscillating signal; it is computationally simple and requires no carrier phase information, making it suitable for narrowband signals. The original oscillation envelope is downsampled by integer multiples to obtain an instantaneous total amplitude envelope sequence with a sampling rate of 8~10Hz. .

[0037] S3: Calculate the frequency split of the hemispherical harmonic oscillator based on the instantaneous total amplitude envelope sequence; Specifically, frequency fragmentation is calculated using the conventional envelope method. (referred to as frequency splitting) can be determined by performing FFT on the acquired data, or by performing envelope FFT analysis on the beat frequency when the frequency splitting is small, to find the main peak of the beat frequency, thereby obtaining the frequency splitting. .

[0038] If the calculated frequency split is 0, proceed directly to step S5.3.

[0039] S4: Determine the sliding window width based on the frequency splitting, then extract the upper envelope of the instantaneous total amplitude envelope sequence based on the sliding window width, and calculate the envelope wave modulation depth; Specifically, the sliding window width is determined based on frequency splitting, including: sliding window width ,in It is a frequency crack.

[0040] Specifically, calculating the envelope wave modulation depth includes: Envelope wave modulation depth , , These represent the maximum and minimum envelope values ​​of the instantaneous total amplitude envelope sequence within the sliding window width, respectively.

[0041] The detailed explanation of step S4 is as follows: Determine the width Nwin of the sliding window on one side; its span should be slightly larger than half a beat frequency cycle as roughly measured. ).

[0042] The upper envelope of the signal is extracted using the max-pooling operator, ensuring that the maximum value within the window Nwin is always taken, thus completely eliminating valley points and stripping away the purely exponentially decaying outer shell, thereby obtaining the upper envelope. .

[0043] , where i is the i-th index time of the pooling envelope.

[0044] Then through the non-monotonic fluctuation depth of the envelope (modulation depth) This is used to adaptively categorize the beat frequency intensity into three levels.

[0045] S5: If the envelope wave modulation depth is greater than 50%, proceed to step S5.1; if the envelope wave modulation depth is within the range of 5%-50%, proceed to step S5.2; if the envelope wave modulation depth is less than 5%, proceed to step S5.3. S5.1: After taking the logarithm of the upper envelope, perform univariate linear regression fitting, calculate the quality factor of the hemispherical harmonic oscillator based on the obtained fitting parameters, and then terminate and exit. Specifically, regarding the upper envelope After taking the logarithm, a univariate linear regression is performed, specifically including: ,in, For the upper envelope, , and represent the slope and intercept of the univariate linear regression equation, respectively, where t is time.

[0046] The quality factor of the hemispherical harmonic oscillator is calculated based on the obtained fitting parameters, specifically including: quality factor. .

[0047] S5.2: Apply a penalty shrinkage factor to the sliding window width, re-extract the upper envelope of the instantaneous total amplitude envelope sequence with the shrunken sliding window width, take the logarithm of the upper envelope and perform univariate linear regression fitting, calculate the quality factor of the hemispherical harmonic oscillator based on the obtained fitting parameters, and then end and exit. Specifically, punitive contractile factor Width of the shrunk sliding window .

[0048] The methods for calculating the fit and quality factor are the same as in step S5.1.

[0049] S5.3: Calculate the quality factor of the hemispherical harmonic oscillator using the time-domain full-lifetime definite integral method, then exit. Specifically, this includes: Calculate the instantaneous energy curve of the filtered pure time-domain signal. Perform time-domain definite integral and time-weighted integral on the instantaneous energy curve within the effective lifetime. Calculate the quality factor of the hemispherical harmonic oscillator based on the time-domain definite integral and time-weighted integral.

[0050] In this embodiment, the instantaneous energy curve definite integral in the time domain Time-weighted integral The effective lifespan of the hemispherical harmonic oscillator is [0, T], and the quality factor of the hemispherical harmonic oscillator is... .

[0051] The following is a detailed explanation of step S5: By modulation depth The signals are divided into three categories: Strong beat frequency signal: The envelope exhibits a deep "W" shape, repeatedly dipping to near the zero baseline. Directly taking the logarithm for linear fitting at this point will completely collapse due to the non-monotonicity of the envelope. The criterion is: >50%.

[0052] Medium beat frequency signal: The envelope monotonically decreases over time, but it is superimposed with obvious sinusoidal "ripple" fluctuations. The criterion is: 5% ≤ ≤ 50%.

[0053] Beatless signals: The beat frequency modulation depth is extremely weak (approaching 0), and the signal physically degenerates into a perfect single-mode pure exponential dissipation. The criterion is: <5%.

[0054] Based on the classification of beat frequency signals, different methods are used to calculate the Q value.

[0055] (1) such as Figure 1 As shown, when the signal is a strong beat frequency signal, the following steps are performed: upper envelope Perform logarithmic transformation and univariate linear regression: , Calculate the quality factor .

[0056] (2) For example Figure 2 As shown, when the signal is a medium beat frequency signal, due to the continuous attenuation of the signal amplitude and the superposition of external interference, the peak of the signal is pulled downwards and becomes asymmetrical. This results in errors when the peak is directly used to fit the Q value.

[0057] At medium beat frequencies, sinusoidal fluctuations are relatively weak. If noise is high, the main peak frequency found by a rough FFT measurement may have a slight bias. In this case, if the program blindly executes the MaxPool with an excessively large window without differentiation, it is very easy to "forcefully stretch" the normal monotonic decay curve caused by Q-value dissipation into a flat-top line (i.e., excessive smoothing distortion) when the data acquisition time is short, resulting in a systematically large calculated Q value.

[0058] Therefore, a security degradation defense and a punitive window contraction are employed. The calculated theoretical window Nwin must be so large that its width on one side absolutely cannot exceed one-third of the current total number of data points N (corresponding to no more than 2 / 3 of the entire window). This ensures that when the sliding window scrolls along the time axis, it leaves at least 1 / 3 of the degrees of freedom within the entire data segment to capture the downward trend of damped exponential dissipation, fundamentally preventing the extreme case where the entire signal is stretched into a single horizontal line.

[0059] At a moderate beat frequency, a penalty contraction factor η is activated. The weaker the beat frequency ( The smaller the value, the closer it is to pure exponential decay, and the lower the demand for filling the valley. In this case, the window should be actively narrowed.

[0060] , when When it approaches 50% (close to the strong beat frequency), η approaches 1.0 (no contraction).

[0061] when When the beat frequency approaches 5% (very weak beat frequency), η approaches 0.5 (physical half-cycle penalty contraction). .

[0062] The subsequent calculation process is the same as the strong beat frequency calculation process.

[0063] (3) such as Figure 3 As shown, when the signal is a beatless signal, the beat frequency modulation depth is extremely weak (approaching 0), and the signal physically degenerates into a perfect single-mode pure exponential dissipation.

[0064] In the later stages of free decay, the data exhibits an upward curve distortion at the tail caused by white noise flooring. If the logarithm is taken before fitting the slope... This will cause the slope The absolute value is too small, resulting in a high Q value. However, by using the time-domain lifetime definite integral method, the additive random noise with zero mean and instantaneous jitter can cancel each other out during the summation process. Moreover, this calculation method is very lightweight and has an extremely high computational speed.

[0065] First, directly calculate the instantaneous energy curve of the filtered, clean time-domain signal: , Secondly, within the effective lifetime [0,T], the energy is subjected to time-domain definite integral (summation) and time-weighted integral respectively: Time-domain definite integral , Time-weighted integral , Calculate the Q value: .

[0066] Example 2

[0067] This embodiment provides an apparatus for implementing the hemispherical harmonic oscillator quality factor calculation method of Embodiment 1, comprising: The acquisition module is used to acquire the vibration decay signal after the resonant excitation of the hemispherical harmonic oscillator is removed; The preprocessing module is used to preprocess the vibration attenuation signal and extract the instantaneous total amplitude envelope sequence; the frequency splitting calculation module is used to calculate the frequency splitting of the hemispherical harmonic oscillator based on the instantaneous total amplitude envelope sequence. The envelope processing module is used to determine the sliding window width based on frequency splitting, extract the upper envelope of the instantaneous total amplitude envelope sequence based on the sliding window width, and calculate the envelope wave modulation depth. The quality factor calculation module is used to calculate the quality factor of the hemispherical harmonic oscillator when the envelope wave modulation depth is greater than 50%, by taking the logarithm of the upper envelope and performing univariate linear regression fitting, and then exiting based on the obtained fitting parameters; it is also used to apply a penalty contraction factor to the sliding window width when the envelope wave modulation depth is within the range of 5%-50%, re-extract the upper envelope of the instantaneous total amplitude envelope sequence with the contracted sliding window width, take the logarithm of the upper envelope and perform univariate linear regression fitting, and then calculate the quality factor of the hemispherical harmonic oscillator based on the obtained fitting parameters, and then exiting; it is also used to calculate the quality factor of the hemispherical harmonic oscillator using the time-domain full-lifetime definite integral method when the envelope wave modulation depth is 5%, and then exiting.

[0068] The embodiments described above are merely preferred embodiments of the present invention. The terms "in one embodiment," "in another embodiment," "in yet another embodiment," or "in still another embodiment" used in this specification all refer to one or more of the same or different embodiments according to this disclosure. Ordinary variations and substitutions made by those skilled in the art within the scope of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the quality factor of a hemispherical harmonic oscillator, characterized in that, Includes the following steps: S1: Acquire the vibration decay signal after the resonant excitation of the hemispherical harmonic oscillator is removed; S2: Preprocess the vibration attenuation signal to extract the instantaneous total amplitude envelope sequence; S3: Calculate the frequency split of the hemispherical harmonic oscillator based on the instantaneous total amplitude envelope sequence; S4: Determine the sliding window width based on the frequency splitting, then extract the upper envelope of the instantaneous total amplitude envelope sequence based on the sliding window width, and calculate the envelope wave modulation depth; S5: If the envelope wave modulation depth is greater than 50%, proceed to step S5.1; if the envelope wave modulation depth is within the range of 5%-50%, proceed to step S5.2; if the envelope wave modulation depth is less than 5%, proceed to step S5.

3. S5.1: After taking the logarithm of the upper envelope, perform univariate linear regression fitting, calculate the quality factor of the hemispherical harmonic oscillator based on the obtained fitting parameters, and then terminate and exit. S5.2: Apply a penalty shrinkage factor to the sliding window width, re-extract the upper envelope of the instantaneous total amplitude envelope sequence with the shrunken sliding window width, take the logarithm of the upper envelope and perform univariate linear regression fitting, calculate the quality factor of the hemispherical harmonic oscillator based on the obtained fitting parameters, and then end and exit. S5.3: Calculate the quality factor of the hemispherical harmonic oscillator using the time-domain full-lifetime definite integral method, then end and exit; In step S4, the envelope wave modulation depth is calculated, specifically including: Envelope wave modulation depth , , These are the maximum and minimum envelope values ​​of the instantaneous total amplitude envelope sequence within the sliding window width, respectively.

2. The method for calculating the quality factor of a hemispherical harmonic oscillator according to claim 1, characterized in that, Step S3 further includes: if frequency splitting = 0, proceed to step S5.

3.

3. The method for calculating the quality factor of a hemispherical harmonic oscillator according to claim 1 or 2, characterized in that, Step S2 specifically includes: S2.1: Cascaded FIR downsampling filtering is used to reduce the sampling rate of the vibration attenuation signal to 20-30kHz; S2.2: Perform a short-time Fourier transform on the downsampled vibration attenuation signal to obtain its operating frequency range; S2.3: Within the operating frequency range, a robust regression algorithm is used to fit the absolute frequency drift rate. Then, the center frequency is calculated based on the absolute frequency drift rate compensation. Based on the center frequency, the downsampled vibration attenuation signal is subjected to multi-order Butterworth bandpass filtering. The filtering result is then subjected to Hilbert envelope transform to obtain the analytical signal. The original oscillation envelope sequence is obtained by taking the modulus of the analytical signal. The original oscillation envelope sequence is downsampled by an integer multiple to obtain the instantaneous total amplitude envelope sequence with a sampling rate of 8-10Hz.

4. The method for calculating the quality factor of a hemispherical harmonic oscillator according to claim 3, characterized in that, In step S2.3, based on the absolute frequency drift rate The compensation calculation of the center frequency specifically includes: calculating the center frequency using the dynamic time-domain midpoint compensation method. , The starting frequency of the downsampled vibration attenuation signal. The absolute frequency drift rate, Sampling time.

5. The method for calculating the quality factor of a hemispherical harmonic oscillator according to claim 4, characterized in that, In step S4, the sliding window width is determined based on frequency splitting, specifically including: sliding window width ,in It is a frequency crack.

6. The method for calculating the quality factor of a hemispherical harmonic oscillator according to claim 1, characterized in that, In steps S5.1 and S5.2, the upper envelope is... After taking the logarithm, a univariate linear regression is performed, specifically including: ,in, For the upper envelope, , , respectively, represent the slope and intercept of the univariate linear regression equation, where t is time; The quality factor of the hemispherical harmonic oscillator is calculated based on the obtained fitting parameters, specifically including: quality factor. .

7. The method for calculating the quality factor of a hemispherical harmonic oscillator according to claim 6, characterized in that, In step S5.2, the punitive contraction factor Width of the shrunk sliding window .

8. The method for calculating the quality factor of a hemispherical harmonic oscillator according to any one of claims 4-7, characterized in that, In step S5.3, the quality factor of the hemispherical harmonic oscillator is calculated using the time-domain whole-lifetime definite integral method, specifically including: Calculate the instantaneous energy curve of the filtered pure time-domain signal. Perform time-domain definite integral and time-weighted integral on the instantaneous energy curve within the effective lifetime. Calculate the quality factor of the hemispherical harmonic oscillator based on the time-domain definite integral and time-weighted integral.

9. An apparatus for implementing the method for calculating the quality factor of a hemispherical harmonic oscillator as described in claim 1, characterized in that, include: The acquisition module is used to acquire the vibration decay signal after the resonant excitation of the hemispherical harmonic oscillator is removed; The preprocessing module is used to preprocess the vibration attenuation signal and extract the instantaneous total amplitude envelope sequence; The frequency-fracture calculation module is used to calculate the frequency-fracture of the hemispherical harmonic oscillator based on the instantaneous total amplitude envelope sequence. The envelope processing module is used to determine the sliding window width based on frequency splitting, extract the upper envelope of the instantaneous total amplitude envelope sequence based on the sliding window width, and calculate the envelope wave modulation depth. The quality factor calculation module is used to perform univariate linear regression fitting after taking the logarithm of the upper envelope when the modulation depth of the envelope fluctuation is greater than 50%, calculate the quality factor of the hemispherical harmonic oscillator based on the obtained fitting parameters, and then end and exit. It is also used to apply a penalty shrinkage factor to the sliding window width when the envelope wave modulation depth is judged to be in the range of 5%-50%, and to re-extract the upper envelope of the instantaneous total amplitude envelope sequence with the shrunken sliding window width. After taking the logarithm of the upper envelope, a univariate linear regression is performed to fit it. The quality factor of the hemispherical harmonic oscillator is calculated based on the obtained fitting parameters, and then the process ends and exits. It is also used to calculate the quality factor of the hemispherical harmonic oscillator by using the time-domain full-lifetime definite integral method when the envelope wave modulation depth is 5%, and then terminate and exit.

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