A method and device for identifying frequency split and rigid axis of a hemispherical resonator gyro

Abstract

The application discloses a kind of hemispherical resonator gyro frequency crack and rigid axle identification method and device, method includes: constructing the frequency model of hemispherical resonator gyro by harmonic term and drift term, real-time collection hemispherical resonator gyro mode angle, frequency and temperature data in set time period, and construct linear drift matrix about temperature and time, and construct and solve linear drift matrix about frequency drift parameter identification model, to each measured frequency is removed drift processing, obtain harmonic frequency;Triangular harmonic matrix about mode angle is constructed, and harmonic parameter identification model about harmonic frequency is constructed and solved to triangular harmonic matrix, obtain harmonic parameter matrix;From the obtained harmonic parameter matrix, the harmonic parameter corresponding to the fourth-order harmonic is extracted, and the attribute parameters of the hemispherical resonator gyro are calculated. The application can improve the high-precision identification accuracy of hemispherical resonator gyro frequency crack and rigid axle, and improve the navigation accuracy of subsequent control algorithm.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, specifically to a method and apparatus for identifying frequency cracks and rigid axes in a hemispherical resonant gyroscope. Background Technology

[0002] A hemispherical resonant gyroscope (HRG) is a solid-state vibrating gyroscope that uses a quartz hemispherical shell as its sensing element. Its working principle is based on the n=2 elliptical vibration mode of the quartz hemispherical shell. An ideal hemispherical shell possesses perfect rotational symmetry, with the natural frequencies of the two orthogonal vibration modes being strictly equal. However, in actual manufacturing, material inhomogeneities, geometric errors, and surface defects inevitably disrupt this symmetry, leading to a slight difference in the natural frequencies of the two orthogonal vibration modes, known as frequency splitting (Δf). Frequency splitting is one of the most critical performance indicators of an HRG, its magnitude directly determining the gyroscope's zero-bias error and angular rate measurement accuracy. Another key parameter associated with frequency splitting is the rigid axis azimuth angle (φ), which describes the orientation of the high-frequency vibration mode relative to the shell reference and is the fundamental input for electrode alignment compensation and open-loop / closed-loop control algorithms. If systematic identification errors exist in either of these parameters, the compensated zero bias will exhibit an unavoidable residual error, directly affecting navigation accuracy.

[0003] In the frequency splitting test, the test system drives the mode shape angle θ to monotonically scan in all directions while acquiring frequency signals.

[0004] Frequency signal during HRG second-order mode operation under ideal, drift-free conditions. It can be represented as: , Where θ is the mode angle, A and B are harmonic coefficients, and C0 is the mean bias.

[0005] The frequency splitting amplitude and the rigid axis azimuth angle are derived from A and B: Fission amplitude (peak): , Frequency fragmentation (peak-to-peak value): , Original azimuth angle of rigid shaft: , ;

[0006] In actual test data, the complete signal model of the frequency includes harmonic terms, temperature drift, time drift, and temperature-harmonic interaction terms. Traditional analysis methods construct all influencing factors—harmonic terms, temperature drift, time drift, and their interactions—into a single feature matrix and directly perform global least squares fitting on the original signal. A single call to least squares can complete the estimation of all parameters. This strategy can yield acceptable results under ideal laboratory conditions, but it has a fundamental flaw in engineering testing environments: the mode shape angle θ increases monotonically with time and is highly correlated with temperature drift in the time domain. The superposition energy of the two cannot be correctly allocated through joint least squares, and the drift trend is systematically misattributed to the harmonic coefficients, resulting in a serious overestimation of the frequency fragmentation calculation results. The azimuth angle of the rigid shaft also shows a systematic deviation of about 3° to 10°. This error does not converge with the increase of data volume, has a clear physical cause, and belongs to the structural problem at the algorithm level. Summary of the Invention

[0007] To address the problems in the background art, the present invention provides a method and apparatus for identifying frequency cracks and rigid axes in a hemispherical resonant gyroscope, which can improve the high-precision identification accuracy of frequency cracks and rigid axes in a hemispherical resonant gyroscope and improve the navigation accuracy of subsequent control algorithms.

[0008] The present invention adopts the following technical solution: A method for identifying frequency cracks and rigid axes in a hemispherical resonant gyroscope includes the following steps: A frequency model of a hemispherical resonant gyroscope is constructed. The frequency model consists of harmonic terms with trigonometric functions and drift terms with linear functions. The mode shape angle, frequency, and temperature data of the hemispherical resonant gyroscope are collected in real time within a set time period. Based on all frequencies and their corresponding temperatures and times, a linear drift matrix with respect to temperature and time is constructed, and a drift parameter identification model of the linear drift matrix with respect to frequency is constructed. The drift parameter identification model is solved to obtain the drift parameter matrix. Based on the obtained drift parameter matrix, the measured frequencies are de-drifted to obtain the harmonic frequencies. Construct a triangular harmonic matrix with respect to mode angles, and construct a harmonic parameter identification model of the triangular harmonic matrix with respect to harmonic frequencies. Solve the harmonic parameter identification model to obtain the harmonic parameter matrix. The harmonic parameters corresponding to the fourth harmonic are extracted from the obtained harmonic parameter matrix, and the attribute parameters of the hemispherical resonant gyroscope are calculated.

[0009] Preferably, the frequency model is frequency. Where θ is the mode angle and i is the harmonic order. For normalized time index, dT represents the temperature fluctuation, where the harmonic term of the trigonometric function relationship is... Among them, the harmonic parameter matrix The drift term of a linear relationship ,in, Here is the drift parameter matrix. .

[0010] Preferably, the linear drift matrix with respect to temperature and time The drift parameter identification model is During the solution process The measured frequency was used as the input.

[0011] Preferably, solving the drift parameter identification model specifically includes: using the least squares regression method to fit and solve the model. Its analytical solution is .

[0012] Preferably, the measured frequencies are de-drifted based on the obtained drift parameter matrix to obtain the harmonic frequencies, specifically including: .

[0013] Preferably, the triangular harmonic matrix with respect to the mode angle The harmonic parameter identification model is .

[0014] Preferably, solving the harmonic parameter identification model specifically includes: using the Ridge regression method, introducing a regularized intensity alpha, and for each candidate alpha value, using leave-one-out cross-validation to fit the harmonic parameter identification model, selecting the analytical solution corresponding to the alpha with the smallest Ridge error, wherein... The analytical solution is , where I is the identity matrix.

[0015] Preferably, the attribute parameters include the fracture amplitude, frequency fracture, and the original azimuth angle of the rigid axis.

[0016] The formula for calculating the pyrolysis amplitude is: Pyrolysis Amplitude ; The formula for calculating frequency splitting is: Frequency splitting ; The formula for calculating the original azimuth angle of a rigid shaft is: Original azimuth angle of a rigid shaft , ; in, , These are the harmonic parameters corresponding to the fourth harmonic.

[0017] Preferably, before constructing the drift parameter identification model, the method further includes: processing the collected data, specifically including: removing data whose collected temperature is outside the set temperature range, removing data whose collected frequency is outside the set effective frequency range, and processing the data according to the set reference temperature. The collected temperature is converted into temperature fluctuation dT.

[0018] Preferably, the effective frequency range is determined using the following method: Using an interquartile range, all frequencies are divided into four equal parts from largest to smallest. Q1 = 25% quantile and Q3 = 75% quantile are selected, and IQR = Q3 - Q1 is calculated. The effective frequency range is then determined. .

[0019] As a general inventive concept, the present invention also provides an apparatus for implementing the above-described method for identifying the frequency split and rigid axis of a hemispherical resonant gyroscope, comprising: The acquisition module acquires the frequency model of the hemispherical resonant gyroscope, which consists of harmonic terms with trigonometric functions and drift terms with linear functions, and acquires the mode shape angle, frequency and temperature data of the hemispherical resonant gyroscope within a set time period. The first solution module constructs a linear drift matrix with respect to temperature and time based on all frequencies and their corresponding temperatures and times, and constructs a drift parameter identification model of the linear drift matrix with respect to frequency. It solves the drift parameter identification model to obtain the drift parameter matrix, and performs de-drift processing on each measured frequency based on the obtained drift parameter matrix to obtain the harmonic frequencies. The second solution module constructs a triangular harmonic matrix with respect to the mode angle, and constructs a harmonic parameter identification model of the triangular harmonic matrix with respect to the harmonic frequency. The harmonic parameter identification model is solved to obtain the harmonic parameter matrix. The extraction and calculation module extracts the harmonic parameters corresponding to the fourth harmonic from the obtained harmonic parameter matrix and calculates the attribute parameters of the hemispherical gyroscope.

[0020] Compared with the prior art, the advantages of the present invention are as follows: The identification method for frequency splits and rigid axes of hemispherical resonant gyroscopes in this invention constructs a drift characteristic matrix free of any harmonic terms, ensuring that least squares can only attribute drift energy to drift coefficients without mistakenly extracting harmonic energy from the frequency data. Harmonic fitting is then performed on the drift-free pure signal, further resolving the harmonic coefficient contamination caused by drift, thereby improving the high-precision identification accuracy of frequency splits and rigid axes in hemispherical resonant gyroscopes. Attached Figure Description

[0021] 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.

[0022] Figure 1 This is a flowchart of the method for identifying frequency cracks and rigid axes in a hemispherical resonant gyroscope according to an embodiment of the present invention.

[0023] Figure 2The images show the original data and the filtered data used in this embodiment of the invention.

[0024] Figure 3 This is a drift estimation diagram according to an embodiment of the present invention.

[0025] Figure 4 This is a diagram illustrating the identification of frequency cracking and rigid shaft angle in an embodiment of the present invention.

[0026] Figure 5 This is a graph showing the data drift removal and fitting results of an embodiment of the present invention. Detailed Implementation

[0027] 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.

[0028] Commonly used calculation methods for frequency cracks and rigid shafts construct all features (harmonics + drift + interaction) into the same feature matrix at once, and perform global least squares fitting on the original frequency test data. A single call to the least squares method can complete the estimation of all parameters. The accuracy is acceptable when the drift magnitude is much smaller than the harmonic amplitude, but the error is large when the drift magnitude is large, making it unsuitable.

[0029] Therefore, the drift contamination problem during the joint fitting of the above features needs to be considered. Let's assume, in practical cases, the HRG frequency signal... It consists of harmonic terms and linear drift: , Where bθ is the linear drift term, and since θ is monotonically increasing, b is the linear drift coefficient. bθ and sin(4θ) / cos(4θ) have a non-zero correlation in the sample space. Let the feature matrix... Its Gram matrix X T X has non-zero, non-diagonal elements: ,in When the period is incomplete, the mode angles of j at different positions.

[0030] Normal equation In the solution (where K is the solution coefficient), the sinusoidal component of K under ideal conditions and the cosine component of K The projected components of the bθ term will be disturbed, that is, the sinusoidal components of K in reality. The cosine component of K in actual situations .

[0031] Increment of coefficient A amplitude (Approximate deviation after correlation), Δb is the bias increment.

[0032] exist Orthogonality holds true for whole periods (deviation is zero), but in actual measurements, the data often covers non-integer multiples of the period or the data density is uneven, which destroys the orthogonality and the deviation cannot be ignored.

[0033] In the test, the frequency monotonically increases and is highly correlated with time t; the temperature T(t) also changes monotonically with t. The least squares method cannot correctly allocate the contribution of each column when the column vectors of the characteristic matrix are correlated; the drift energy is greedily absorbed into the sin(4θ) / cos(4θ) coefficients, causing frequency distortion in the calculation. At the same time, the linear trend of the drift, superimposed on the harmonics, introduces a phase shift, causing distortion of the rigid axis in the calculation.

[0034] To address the aforementioned problems, this invention abandons the traditional joint fitting strategy and adopts a two-step decoupling scheme that first removes drift and then fits harmonics: The first step involves constructing a strictly harmonic-free drift characteristic model (temperature polynomial + normalized time polynomial) to estimate and remove the drift trend from the original signal, resulting in a drift-free pure signal. The second step involves performing harmonic fitting only on the pure signal. At this point, the harmonic coefficients are completely unaffected by drift energy, and the estimation of frequency fragmentation and rigid axis azimuth is fundamentally accurate. Based on this, a residual refinement step with temperature-harmonic interaction terms is added to further capture the temperature modulation effect.

[0035] Specifically, such as Figure 1 As shown, this invention proposes a method for identifying frequency cracks and rigid axes in a hemispherical resonant gyroscope, comprising the following steps: A frequency model of a hemispherical resonant gyroscope is constructed. The frequency model consists of harmonic terms with trigonometric functions and drift terms with linear functions. The mode shape angle, frequency, and temperature data of the hemispherical resonant gyroscope are collected in real time within a set time period. The collected data is processed, specifically including: removing data whose temperature is outside the set temperature range, removing data whose frequency is outside the set effective frequency range, and processing the data based on the set reference temperature. The collected temperature is converted into a temperature fluctuation dT. Based on all frequencies and their corresponding processed temperature and time data, a linear drift matrix with respect to temperature and time is constructed, and a drift parameter identification model of the linear drift matrix with respect to frequency is constructed. The drift parameter identification model is solved to obtain the drift parameter matrix. Based on the obtained drift parameter matrix, the measured frequencies are de-drifted to obtain the harmonic frequencies. Construct a triangular harmonic matrix with respect to mode angles, and construct a harmonic parameter identification model of the triangular harmonic matrix with respect to harmonic frequencies. Solve the harmonic parameter identification model to obtain the harmonic parameter matrix. The harmonic parameters corresponding to the fourth harmonic are extracted from the obtained harmonic parameter matrix, and the attribute parameters of the hemispherical resonant gyroscope are calculated.

[0036] Therefore, by constructing a drift characteristic matrix that contains no sin / cos harmonic terms, least squares can only attribute drift energy to the drift coefficients, without mistakenly extracting harmonic energy from the frequency data. Harmonic fitting is then performed on the drift-free clean signal, and the sin / cos coefficients are no longer contaminated by drift.

[0037] This invention takes into account practical calculation requirements and models the measured frequency signal according to the following formula: .

[0038] in This represents the temperature fluctuation, where T is the current temperature. The initial temperature, Here, α, β, and γ represent the normalized time index, α, β, and γ are the fitting coefficients, the subscript numbers indicate the corresponding polynomial order, and i represents the i-th harmonic order. The portion of the formula containing sine and cosine terms represents a pure signal close to the ideal state, while the rest represents the drift signal. The coupling between the drift term and the harmonic term is the fundamental source of the difference between the two algorithms.

[0039] Among them, the harmonic terms of trigonometric function relationships Among them, the harmonic parameter matrix The drift term of a linear relationship ,in, Here is the drift parameter matrix. .

[0040] Applying the above model, in frequency splitting tests, it can effectively solve the problem that the target frequency signal Fq output by the gyroscope changes with the mode angle θ as a 4-fold period, while simultaneously being superimposed with temperature drift and time drift, thus achieving high-precision identification of frequency splitting and rigid shaft angle.

[0041] In this embodiment, the linear drift matrix with respect to temperature and time... The drift parameter identification model is During the solution process The measured frequency was used as the input.

[0042] In this embodiment, solving the drift parameter identification model specifically includes: using the least squares regression method to fit and solve the model. Its analytical solution is .

[0043] In this embodiment, the measured frequencies are de-drifted based on the obtained drift parameter matrix to obtain the harmonic frequencies, specifically including: .

[0044] In this embodiment, the triangular harmonic matrix regarding the mode angle The harmonic parameter identification model is .

[0045] The residuals may contain a weak temperature modulation effect. This invention uses a temperature-harmonic interaction term for further refinement to improve the identification accuracy.

[0046] In this embodiment, solving the harmonic parameter identification model specifically includes: using the Ridge regression method and introducing a regularization intensity alpha (ranging from...). For each candidate alpha value, leave-one-out cross-validation is used to fit the harmonic parameter identification model, and the analytical solution corresponding to the alpha with the smallest ridge error is selected. The analytical solution is , where I is the identity matrix.

[0047] Adding Ridge regularization can automatically perform Ridge on the drift-de-switching signal when the data signal is extremely weak. Automatic LOO-CV search for alpha prevents numerical instability in harmonic coefficient estimation when the signal is weak, thereby ensuring reliable output of frequency split amplitude and rigid axis azimuth angle.

[0048] The goal of ordinary least squares is to minimize the sum of squared residuals: Its analytical solution is: , Where y is the target observation vector, X is the feature matrix, K is the parameter vector to be determined, and T is the transpose.

[0049] When the de-drifted harmonic signal is extremely weak (e.g., Δf is only about 0.001 Hz), or when there is a slight correlation between the column vectors of the characteristic matrix, matrix X T X approaches singularity, and its inverse matrix is ​​numerically unstable, leading to a sharp increase in the variance of the coefficient estimates, a phenomenon known as overfitting.

[0050] Ridge regression adds an L2 penalty term based on the magnitude of the coefficients to the sum of squared residuals: alpha represents the regularization strength, which controls the penalty intensity. Its analytical solution becomes: I is the identity matrix.

[0051] Adding alpha×I ensures that matrix inversion remains numerically stable, and the coefficients are not abnormally amplified due to eigencorrelation or weak signals. The trade-off is the introduction of a small bias (coefficients are compressed), but this results in a significant reduction in variance.

[0052] Initially, a range of alpha values ​​is given. For each candidate alpha value, leave-one-out cross-validation (LOO-CV) is used to evaluate the model's prediction error on unseen data points at that alpha value. The model with the highest error is then selected. The minimum alpha value is substituted into the formula to be fitted, and the amplitude, frequency split, and rigid axis azimuth angle are finally calculated.

[0053] In this embodiment, the attribute parameters include the fracture amplitude, frequency fracture, and the original azimuth angle of the rigid axis.

[0054] The formula for calculating the pyrolysis amplitude is: Pyrolysis Amplitude ; The formula for calculating frequency splitting is: Frequency splitting ; The formula for calculating the original azimuth angle of a rigid shaft is: Original azimuth angle of a rigid shaft , ; This method is applicable to calculation scenarios where the frequency drift is greater than 0.5 times the split amplitude; and it is applicable not only to complete hemispherical resonator gyroscopes, but also to the frequency splitting and high-precision identification of semi-finished hemispherical resonator gyroscopes.

[0055] The following examples further illustrate the process by which this invention achieves high-precision identification of frequency breakage in hemispherical resonant gyroscopes and rigid axes: (1) Fix the 0° position of the main body of the hemispherical resonant gyroscope; this 0° position is also the reference zero position for confirming the azimuth angle of the standing wave during the test; (2) Confirm that the vacuum level of the environment in which the measuring subject is located is 1E-4Pa or better; (3) Using circuitry and control algorithms, measure the frequency data of the hemispherical resonant gyroscope within at least one period in the time series, including temperature data; (4) Data export; (5) Use the following process to analyze and fit the data using programming languages ​​such as Python or MATLAB. The results are as follows: Figure 2 As shown: A) Data loading and format validation. The data to be read must contain three data columns: θ (mode angle), frequency, and temperature; where θ is monotonically increasing scan data. Formula for constructing frequency data .

[0056] B) Temperature filtering and interquartile range (IQR) outlier removal remove physically unreasonable data points to ensure the robustness of subsequent fitting.

[0057] First, apply physical constraints to the temperature column and remove rows that clearly exceed the sensor's range or are recorded incorrectly, such as limiting the temperature to -40℃ to 100℃. After temperature filtering, statistical outlier removal is performed on the target frequency to prevent extreme outliers introduced by equipment vibration or recording errors from interfering with the fitting results. The judgment criteria for the IQR method are as follows: The interquartile range is used, which means that the entire frequency data is evenly divided into four parts from large to small. Q1 = 25% frequency data quantile, Q3 = 75% frequency data quantile, IQR = Q3-Q1.

[0058] Valid range: The default value k = 1.5 (strict), which can be set to 3.0 (lenient) to remove outliers based on the valid range.

[0059] C) Temperature reference debiasing: converting absolute temperature into relative temperature fluctuations reduces pathological problems caused by numerical range.

[0060] The temperature of the first valid data point in the test sequence is taken as the reference temperature. The temperature of all subsequent data points is converted into a relative fluctuation dT.

[0061] (Test starting temperature); (Temperature fluctuation, in °C, initial value 0).

[0062] D) Pre-removal of drift, the result is as follows Figure 3 As shown: The mode shape angle θ increases monotonically during the test, and the temperature also changes monotonically with time. If the fourth harmonic of the original frequency containing the drift is directly identified, the low-frequency energy of the drift will form a significant DC component and low-frequency peak in the spectrum, interfering with the harmonic identification. Therefore, a pre-drift removal process must be performed before identification to obtain a pre-processed signal after drift removal.

[0063] Construct a drift characteristic matrix that is strictly free of any harmonic terms. It contains only temperature polynomials and normalized time polynomials: , Vector coefficient matrix , Pre-drift processing data .

[0064] Since the frequency signal is defined as consisting of a linear drift term and trigonometric harmonic terms, and the drift term is composed only of temperature variation and a time polynomial, while the harmonic terms are composed of trigonometric relationships, a matrix of temperature variation and a time polynomial is used. When fitting frequencies, only the drift term is included in the coefficient calculation, meaning the coefficients of the linear term can be fitted, but the coefficients of the triangular harmonics cannot be fitted. By subtracting the linear drift term from each original frequency, a pure harmonic curve is obtained. Fitting this pure harmonic curve then yields the coefficients of the harmonic terms.

[0065] E) Weak signal detection and Ridge decision: Determine whether the harmonic signal after drift removal is weak and decide whether to enable Ridge regularization. LOO-CV (Leave-one-out cross-validation): For each candidate alpha value, remove one data point in turn, fit the Ridge model with the remaining N-1 points, predict the removed points, and calculate the average error.

[0066] Frequency splitting is typically at the mHz level, which falls under the category of weak signal detection. Therefore, this step is performed during subsequent harmonic fitting.

[0067] F) Two-step decoupled fitting and physical parameter extraction: first, drift is removed; then, harmonics are fitted; finally, frequency fragmentation and rigid axis are extracted. The results are as follows: Figure 4 and Figure 5 As shown.

[0068] Pre-drift processing data ;

[0069] Constructing multi-harmonic order matrices .

[0070] At this point, residual temperature-harmonic interaction refinement should be considered: The residuals may still contain the temperature modulation effect on harmonic amplitudes (i.e., the magnitude of frequency fragmentation itself changes slightly with temperature). A second-order correction to the multi-harmonic order matrix yields: Second-order corrected data matrix ; Using matrices Substitution ,get Matrix. From Extracting the coefficients corresponding to the 4θ harmonic from the matrix , Using these as coefficients A and B respectively, the amplitude, frequency split, and rigid axis azimuth angle are calculated using the aforementioned formula.

[0071] (6) Using the reference zero position of the azimuth angle found in step (1), the corresponding rigid shaft angle is found for use in the next stage, such as for quality leveling and control algorithms. In the control algorithm, multiple sets of frequency cracks and rigid shaft angles are identified at different temperature points and solidified into a one-dimensional temperature lookup table in the FPGA. When the circuit is working, the temperature is read in real time through the current temperature control sensor, and the corresponding stiffness matrix defect unit is interpolated and demodulated to achieve high-precision control in the entire temperature range.

[0072] 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 identifying frequency cracks and rigid axes in a hemispherical resonant gyroscope, characterized in that, Includes the following steps: A frequency model of a hemispherical resonant gyroscope is constructed. The frequency model consists of harmonic terms with trigonometric functions and drift terms with linear functions. The mode shape angle, frequency, and temperature data of the hemispherical resonant gyroscope are collected in real time within a set time period. Based on all frequencies and their corresponding temperatures and times, a linear drift matrix with respect to temperature and time is constructed, and a drift parameter identification model of the linear drift matrix with respect to frequency is constructed. The drift parameter identification model is solved to obtain the drift parameter matrix. Based on the obtained drift parameter matrix, the measured frequencies are de-drifted to obtain the harmonic frequencies. Construct a triangular harmonic matrix with respect to mode angles, and construct a harmonic parameter identification model of the triangular harmonic matrix with respect to harmonic frequencies. Solve the harmonic parameter identification model to obtain the harmonic parameter matrix. The harmonic parameters corresponding to the fourth harmonic are extracted from the obtained harmonic parameter matrix, and the attribute parameters of the hemispherical resonant gyroscope are calculated. Frequency model is frequency Where θ is the mode angle and i is the harmonic order. For normalized time index, dT represents the temperature fluctuation, where the harmonic term of the trigonometric function relationship is... Among them, the harmonic parameter matrix The drift term of a linear relationship ,in, Here is the drift parameter matrix. ; The first harmonic sine coefficient, The first harmonic cosine coefficient, The second harmonic sine coefficients are... The second harmonic cosine coefficient, The third harmonic sine coefficients, The third harmonic cosine coefficients, The fourth harmonic sine coefficients are... The fourth harmonic cosine coefficient, These are the second-order modified first-order harmonic sine coefficients. These are the second-order modified first-order harmonic cosine coefficients. These are the second-order harmonic sine coefficients with second-order correction. These are the second-order harmonic cosine coefficients with second-order correction. These are the second-order modified third-order harmonic sine coefficients. These are the second-order modified third-order harmonic cosine coefficients. These are the second-order corrected fourth-order harmonic sine coefficients. These are the second-order modified fourth-order harmonic cosine coefficients. These are harmonic parameter constants; It is the first-order temperature drift coefficient. It is the second-order temperature drift coefficient. The first-order time drift coefficient, The second-order time drift coefficient, The third-order time drift coefficient, The drift parameter is a constant; It is the sum of the harmonic parameter constant and the drift parameter constant; Linear drift matrix with respect to temperature and time The drift parameter identification model is During the solution process The measured frequency was used as the input.

2. The method for identifying frequency breakage and rigid axis of a hemispherical resonant gyroscope according to claim 1, characterized in that, Solving the drift parameter identification model specifically includes: using the least squares regression method to fit and solve the model. Its analytical solution is .

3. The method for identifying frequency breakage and rigid axis of a hemispherical resonant gyroscope according to claim 2, characterized in that, Based on the obtained drift parameter matrix, the measured frequencies are de-drifted to obtain the harmonic frequencies, specifically including: .

4. The method for identifying frequency breakage and rigid axis of a hemispherical resonant gyroscope according to any one of claims 1-3, characterized in that, Regarding the trigonometric harmonic matrix of mode angles The harmonic parameter identification model is .

5. The method for identifying frequency breakage and rigid axis of a hemispherical resonant gyroscope according to claim 4, characterized in that, Solving the harmonic parameter identification model specifically includes: employing the Ridge regression method, introducing a regularized intensity alpha, and for each candidate alpha value, using leave-one-out cross-validation to fit the harmonic parameter identification model. The analytical solution corresponding to the alpha value with the smallest Ridge error is then selected. The analytical solution is , where I is the identity matrix.

6. The method for identifying frequency breakage and rigid axis of a hemispherical resonant gyroscope according to any one of claims 1-3, characterized in that, The attribute parameters include the fracture amplitude, frequency fracture, and the original azimuth angle of the rigid axis. The formula for calculating the pyrolysis amplitude is: Pyrolysis Amplitude ; The formula for calculating frequency splitting is: Frequency splitting ; The formula for calculating the original azimuth angle of a rigid shaft is: Original azimuth angle of a rigid shaft , ; in, , These are the harmonic parameters corresponding to the fourth harmonic.

7. The method for identifying frequency breakage and rigid axis of a hemispherical resonant gyroscope according to any one of claims 1-3, characterized in that, Before constructing the drift parameter identification model, the process also includes: processing the collected data, specifically including: removing data whose collected temperature is outside the set temperature range, removing data whose collected frequency is outside the set effective frequency range, and processing the data based on the set reference temperature. The collected temperature is converted into temperature fluctuation dT.

8. An apparatus for implementing the identification method of frequency breakage and rigid axis of a hemispherical resonant gyroscope as described in claim 1, characterized in that, include: The acquisition module acquires the frequency model of the hemispherical resonant gyroscope, which consists of harmonic terms with trigonometric functions and drift terms with linear functions, and acquires the mode shape angle, frequency and temperature data of the hemispherical resonant gyroscope within a set time period. The first solution module constructs a linear drift matrix with respect to temperature and time based on all frequencies and their corresponding temperatures and times, and constructs a drift parameter identification model of the linear drift matrix with respect to frequency. It solves the drift parameter identification model to obtain the drift parameter matrix, and performs de-drift processing on each measured frequency based on the obtained drift parameter matrix to obtain the harmonic frequencies. The second solution module constructs a triangular harmonic matrix with respect to the mode angle, and constructs a harmonic parameter identification model of the triangular harmonic matrix with respect to the harmonic frequency. It solves the harmonic parameter identification model to obtain the harmonic parameter matrix. The extraction and calculation module extracts the harmonic parameters corresponding to the fourth harmonic from the obtained harmonic parameter matrix and calculates the attribute parameters of the hemispherical gyroscope.

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