Ultra-high efficiency accelerometer sensitivity dynamic calibration method based on multi-frequency sinusoidal excitation

Abstract

A kind of ultra-high efficiency accelerometer sensitivity dynamic calibration method based on multi-frequency sine excitation.It includes constructing wideband accelerometer sensitivity calibration system;Based on logarithmic interval frequency distribution method and enhanced hippo optimization algorithm, the multi-frequency sine excitation signal is optimized;Collecting the voltage signal of charge amplifier and the accelerometer to be calibrated;Based on five-parameter sine approximation method, the frequency, amplitude and phase of each frequency point are solved;Using comparison method to calculate the amplitude and phase sensitivity of the accelerometer to be calibrated at each frequency point and other steps.The method is efficient, stable and has high calibration precision, and can be used for one-time sensitivity calibration of accelerometer under wideband calibration conditions.The logarithmic interval frequency distribution method is used to obtain low harmonic distortion multi-frequency sine excitation signal to improve the calibration precision.The improved hippo optimization algorithm is used to improve the convergence speed and global search ability, and increase the measurement range.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and vibration sensor metrology technology, and particularly relates to a high-efficiency, high-precision, stable and reliable dynamic calibration method for accelerometers under wide-bandgap calibration conditions. Background Technology

[0002] Accelerometers, a type of sensor, are commonly used as fundamental devices for measuring dynamic parameters and are key components of mechanical condition monitoring, structural health monitoring, and fault diagnosis systems. They are currently widely used in critical infrastructure sectors such as bridges, tunnels, hydraulic structures, and port machinery. However, during long-term operation, these sensors are susceptible to sensitivity drift due to environmental temperature fluctuations, mechanical fatigue, and other stress factors. Failure to calibrate them promptly can lead to misjudgments, increased maintenance costs, and even structural safety hazards. Therefore, regular calibration of accelerometers is crucial to ensuring their accuracy and reliability.

[0003] Commonly used accelerometer sensitivity calibration methods include laser interferometry, machine vision, gravity, and comparison methods. Laser interferometry measures the displacement of a reference surface and calibrates the accelerometer by converting displacement to acceleration. Machine vision uses a high-speed camera to capture images of the sensor target or reference mark attached to a vibration platform, measures displacement, and also calibrates the accelerometer using the displacement-acceleration conversion. Gravity measures the accelerometer's response in a gravitational field to calibrate the sensor's sensitivity. The comparison method mounts the accelerometer to be calibrated and a reference accelerometer on the same vibration platform; by comparing their respective output signals, the sensitivity of the sensor under test can be determined. Currently, most of these calibration methods employ single-frequency excitation calibration, which tests only a specific frequency each time, resulting in low efficiency, especially when covering a wide frequency range, making the calibration process more time-consuming and complex. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide a dynamic calibration method for the sensitivity of an ultra-efficient accelerometer based on multi-frequency sinusoidal excitation.

[0005] To achieve the above objectives, the present invention provides an ultra-efficient dynamic calibration method for accelerometer sensitivity based on multi-frequency sinusoidal excitation, comprising the following steps performed in sequence:

[0006] 1) Construct a broadband accelerometer sensitivity calibration system, which includes a data processing and display unit, a signal generator, a power amplifier, an intermediate frequency standard vibration table, a reference accelerometer, an accelerometer to be calibrated, a data acquisition card, and a charge amplifier; wherein, the upper end of the intermediate frequency standard vibration table is provided with a work surface; the accelerometer to be calibrated and the reference accelerometer are fixed on the work surface from top to bottom; the data processing and display unit is electrically connected to the intermediate frequency standard vibration table in sequence through the signal generator and the power amplifier; the data acquisition card is electrically connected to the reference accelerometer through the charge amplifier, and is also electrically connected to the accelerometer to be calibrated and the data processing and display unit;

[0007] 2) The data processing and display unit optimizes the multi-frequency sinusoidal excitation signal based on the logarithmic interval frequency distribution method and the enhanced hippo optimization algorithm, and controls the signal generator to output the optimized multi-frequency sinusoidal excitation signal. Then, the signal is amplified by the power amplifier and drives the worktable of the intermediate frequency standard vibration table to generate multi-frequency sinusoidal vibration. At the same time, the accelerometer to be calibrated and the reference accelerometer maintain the same motion characteristics as the worktable.

[0008] 3) The charge amplifier converts the charge signal generated by the reference accelerometer into a voltage signal; the data acquisition card simultaneously acquires the voltage signals output by the charge amplifier and the accelerometer to be calibrated, and then transmits them to the data processing and display unit;

[0009] 4) The data processing and display unit fits the voltage signal acquired by the data acquisition card based on the five-parameter sinusoidal approximation method, and calculates the frequency, amplitude and phase of each frequency point;

[0010] 5) Based on the frequency, amplitude, and phase of each of the above frequency points, the data processing and display unit uses a comparison method to calculate the amplitude sensitivity and phase sensitivity of the accelerometer to be calibrated at each of the above frequency points, thereby completing one calibration.

[0011] In step 2), the data processing and display unit optimizes the multi-frequency sinusoidal excitation signal based on the logarithmic interval frequency distribution method and the enhanced hippo optimization algorithm as follows:

[0012] 2.1) The logarithmic interval frequency distribution method is used to effectively suppress harmonic interference from multi-frequency sinusoidal excitation signals. The calculation formula is as follows:

[0013]

[0014] Among them, f i Let be the frequency value of the i-th single-frequency sinusoidal component in the multi-frequency sinusoidal excitation signal, and K be the total number of single-frequency sinusoidal components that make up the multi-frequency sinusoidal excitation signal;

[0015] 2.2) Define the signal crest factor as the ratio of the peak value to the RMS value of the time-domain signal:

[0016]

[0017] Among them, V pk V represents the peak value of the time-domain signal. rms The effective value of the time-domain signal;

[0018] 2.3) Set the population size N and the maximum number of iterations T for the enhanced hippo optimization algorithm. max The population position is initialized using random numbers in the interval (0,1), as shown in the following expression:

[0019] Y j =lb j +ο1·(ub j -lb j (7)

[0020] Where ο1 is an N×1 vector of random numbers, where each element is uniformly distributed between 0 and 1, and ub j and lb j These are the upper and lower bounds of the search space for each dimension, respectively; N is the population size; and m is the number of dimensions in the problem.

[0021] The initial population position matrix is ​​represented as follows:

[0022]

[0023] 2.4) Increase the population size N to 2N, use Latin hypercube sampling to evenly distribute the first N populations, and use adaptive lens back learning to expand the search space and explore new areas for the last N populations, thereby improving the diversity and quality of the initial population.

[0024] 2.5) In the process of reducing the peak factor of multi-frequency sinusoidal excitation signal using the enhanced hippo optimization algorithm, a candidate population set of size 2N is first constructed. The fitness function is designed with "minimizing the peak factor of multi-frequency sinusoidal excitation signal" as the objective function, and the fitness value of each candidate population is calculated. Then, the top N populations with the best fitness values ​​are selected and used as the initial population for optimization in the algorithm iteration process. The algorithm is driven by the initial population to complete the subsequent iteration calculations, and finally the peak factor of multi-frequency sinusoidal excitation signal is effectively reduced.

[0025] 2.6) In the later stages of algorithm iteration, an adaptive t-distribution perturbation strategy is used to escape the local optimum of the algorithm, recalculate the fitness value, and compare it with the previous fitness value to retain the best individual;

[0026] 2.7) Determine if the algorithm has reached the maximum number of iterations. If it has, exit the loop, output the optimal phase, and calculate the optimized multi-frequency sinusoidal excitation signal.

[0027] In step 4), the data processing and display unit uses a five-parameter sine approximation method to fit the voltage signal acquired by the data acquisition card, and calculates the frequency, amplitude, and phase of each frequency point using the following method:

[0028] 4.1) Define a five-parameter sinusoidal approximation fitting algorithm model to fit the voltage signals output by the charge amplifier and the accelerometer to be calibrated, obtained through the data acquisition card, and extract the amplitude and phase at each frequency, as shown in the following formula:

[0029]

[0030] Where y(t) is the fitted voltage signal, used to fit the discrete data acquired by the data acquisition card into a continuous function, facilitating signal feature analysis; A i and B i These are the sinusoidal components of the voltage signals output by the charge amplifier (9) and the accelerometer to be calibrated (7), respectively; ω i C is the angular frequency; D is the corresponding linear interference component; and C is the corresponding offset component.

[0031] 4.2) The trend term in the five-parameter sinusoidal approximation fitting algorithm model above is removed using the linear regression method. The mathematical model of the trend term is as follows:

[0032] y trend (t)=C0t+D0(6)

[0033] Solving for C0 and D0 using the least squares method, the signal after removing the trend term is as follows:

[0034] y1(t)=y(t)-(C0t+D0)(7)

[0035] Where C0 and D0 are the initialization parameters of the trend term at the start of nonlinear fitting;

[0036] 4.3) Perform a Fast Fourier Transform on the signal y1(t) after removing the trend term to obtain the FFT spectrum. Select the frequencies corresponding to the first K local maxima to estimate the angular frequency and sine and cosine initialization parameters without the trend term.

[0037] 4.4) After analyzing the FFT spectrum to obtain the initial guess parameters, the five-parameter sinusoidal approximation fitting algorithm model after removing the trend term is optimized to minimize the sum of squared residuals between the model output and the measured data. The residual function is defined as follows:

[0038]

[0039] Where, θ=[A i Bi ,ω i [C,D] represents the parameter vector to be optimized, M is the time series length, and t... m These are actual measured data;

[0040] 4.5) Iteratively update the parameters to be optimized using the Levenberg-Marquardt algorithm, as shown in the following formula:

[0041] θ (iter+1) =θ (iter) -(J T J+λI) -1 J T r(θ (iter) (9)

[0042] Where J is the Jacobian matrix of the residuals with respect to the parameters; r is the residual vector; λ is the damping factor used to control the iteration step size; iter is the current iteration number;

[0043] 4.6) After obtaining the optimal value of each parameter to be optimized, a continuous signal is generated as follows:

[0044]

[0045] in, and These represent the amplitude, angular frequency, and initial phase of the sinusoidal component at the i-th frequency point, respectively.

[0046] In step 5), the data processing and display unit calculates the amplitude sensitivity and phase sensitivity of the accelerometer to be calibrated at each of the aforementioned frequency points based on the frequency, amplitude, and phase of each frequency point using a comparison method. The method for completing one calibration is as follows:

[0047] The amplitude sensitivity of the reference accelerometer is known, while the amplitude sensitivity of the accelerometer to be calibrated is unknown. Using a comparison method, the amplitude and phase of the reference accelerometer and the accelerometer to be calibrated are compared at the same frequency point. The amplitude difference and phase difference collected by the reference accelerometer and the accelerometer to be calibrated at the same frequency point are defined as the amplitude sensitivity and phase sensitivity of the accelerometer to be calibrated, respectively, thereby completing the calibration of the entire frequency band in one go.

[0048] The ultra-efficient dynamic calibration method for accelerometer sensitivity based on multi-frequency sinusoidal excitation provided by this invention has the following beneficial effects:

[0049] (1) The method of the present invention is efficient, stable and has high calibration accuracy. It can be applied to the high-efficiency and high-precision sensitivity calibration of accelerometers under wide frequency band calibration conditions.

[0050] (2) The present invention obtains a low-harmonic-distortion multi-frequency sinusoidal excitation signal by means of logarithmic interval frequency distribution method, so as to improve calibration accuracy.

[0051] (3) The method of the present invention uses an improved hippo optimization algorithm composed of multiple strategies, including Latin hypercube sampling, adaptive lens back learning and adaptive perturbation mechanism, to improve the convergence speed and global search capability of the original algorithm, so that it obtains a multi-frequency sinusoidal excitation signal with a small amplitude with the minimum peak factor of multi-frequency signal as the objective function, thereby increasing the measurement range.

[0052] (4) The method of the present invention is based on the five-parameter sinusoidal approximation method to fit multi-frequency sinusoidal excitation signals. Combined with the comparison method, the frequency, amplitude sensitivity and phase sensitivity of each single-frequency signal of the accelerometer at the selected frequency point can be obtained with only one calibration. Attached Figure Description

[0053] Figure 1 The flowchart of the ultra-efficient accelerometer sensitivity dynamic calibration method based on multi-frequency sinusoidal excitation provided by the present invention is shown below.

[0054] Figure 2 This is a flowchart of the multi-frequency sinusoidal excitation signal optimization method in this invention;

[0055] Figure 3 This is a flowchart of the five-parameter sine approximation fitting algorithm in this invention;

[0056] Figure 4 This is a schematic diagram of the broadband accelerometer sensitivity calibration system constructed in this invention;

[0057] Figure 5 This is a graph showing the voltage fitting results of the signal generator output in an embodiment of the present invention;

[0058] Figure 6-7 This is a diagram showing the dynamic calibration results of the amplitude sensitivity and phase sensitivity of the accelerometer in an embodiment of the present invention. Detailed Implementation

[0059] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0060] like Figure 1 As shown, the ultra-efficient accelerometer sensitivity dynamic calibration method based on multi-frequency sinusoidal excitation provided by the present invention includes the following steps performed in sequence:

[0061] 1) Constructing such Figure 4The broadband accelerometer sensitivity calibration system shown includes a data processing and display unit 1, a signal generator 2, a power amplifier 3, an intermediate frequency standard vibration table 4, a reference accelerometer 6, an accelerometer to be calibrated 7, a data acquisition card 8, and a charge amplifier 9. The intermediate frequency standard vibration table 4 has a worktable 5 at its upper end. The accelerometer to be calibrated 7 and the reference accelerometer 6 are fixed on the worktable 5 from top to bottom. The data processing and display unit 1 is electrically connected to the intermediate frequency standard vibration table 4 via the signal generator 2 and the power amplifier 3. The data acquisition card 8 is electrically connected to the reference accelerometer 6 via the charge amplifier 9, and is also electrically connected to the accelerometer to be calibrated 7 and the data processing and display unit 1.

[0062] 2) The data processing and display unit 1 optimizes the multi-frequency sinusoidal excitation signal based on the logarithmic interval frequency distribution method and the enhanced hippo optimization algorithm to improve the calibration accuracy. It controls the signal generator 2 to output the optimized multi-frequency sinusoidal excitation signal, which is then amplified by the power amplifier 3 and drives the worktable 5 on the intermediate frequency standard vibration table 4 to generate multi-frequency sinusoidal vibration. At the same time, the accelerometer 7 to be calibrated and the reference accelerometer 6 maintain the same motion characteristics as the worktable 5.

[0063] like Figure 2 As shown, the data processing and display unit 1 optimizes the multi-frequency sinusoidal excitation signal based on the logarithmic interval frequency distribution method and the enhanced hippo optimization algorithm as follows:

[0064] 2.1) The multi-frequency sinusoidal excitation signal is composed of multiple standard sinusoidal components of different frequencies. Due to the inherent total harmonic distortion of a single sinusoidal component, simple linear superposition will lead to severe harmonic interference. Therefore, this invention uses a logarithmic interval frequency distribution method to effectively suppress the harmonic interference of the multi-frequency sinusoidal excitation signal. The calculation formula is as follows:

[0065]

[0066] Among them, f i f is the frequency value of the i-th single-frequency sinusoidal component in the multi-frequency sinusoidal excitation signal, K is the total number of single-frequency sinusoidal components that make up the multi-frequency sinusoidal excitation signal, and f min and f max These represent the lower and upper limits of the selected frequency range, respectively; the frequency value f of each single-frequency sine component. iThe frequencies of each sinusoidal component in the multi-frequency sinusoidal excitation signal used to construct the log-interval frequency distribution are the basic input parameters for subsequent stages: they determine the frequency composition of the multi-frequency sinusoidal excitation signal in the signal generation stage, serve as the fixed frequency input for phase optimization in the enhanced hippo optimization algorithm, participate in signal feature extraction as a frequency term in the five-parameter sinusoidal approximation method fitting, and are used point by point when calculating amplitude sensitivity and phase sensitivity using the comparison method, ultimately directly constituting the frequency axis of the full-band calibration result.

[0067] 2.2) The signal crest factor is defined as the ratio of the peak value to the effective value of the time-domain signal, as shown in Equation (2). After determining the frequency of each single-frequency sinusoidal component using the logarithmic interval frequency distribution method, the enhanced hippo optimization algorithm, composed of the Latin hypercube sampling method, the adaptive lens back learning method, and the adaptive t-distribution perturbation strategy, is used to minimize the signal crest factor by adjusting the phase of each single-frequency sinusoidal component, resulting in a time-domain excitation signal with a lower peak value and a relatively higher effective value. The excitation after the signal crest factor is reduced, provided it does not exceed the peak or linear range of the intermediate frequency standard vibration table 4 and the acquisition link (reference accelerometer 6, accelerometer to be calibrated 7, and data acquisition card 8), allows for a higher excitation amplitude. This significantly improves the signal-to-noise ratio of the measurement and reduces the impact of quantization noise and system noise on amplitude estimation, thereby increasing the measurement range.

[0068]

[0069] Among them, V pk V represents the peak value of the time-domain signal. rms The effective value of the time-domain signal;

[0070] 2.3) Set the population size N and the maximum number of iterations T for the enhanced hippo optimization algorithm. max The population position is initialized using random numbers in the interval (0,1), as shown in the following expression:

[0071] Y j =lb j +ο1·(ub j -lb j (11)

[0072] Where ο1 is an N×1 vector of random numbers, where each element is uniformly distributed between 0 and 1, and ub j and lb j These are the upper and lower bounds of the search space for each dimension, respectively; N is the population size; and m is the number of dimensions in the problem.

[0073] The initial population position matrix is ​​represented as follows:

[0074]

[0075] 2.4) Increase the population size N to 2N, use Latin hypercube sampling to evenly distribute the first N populations, and use adaptive lens back learning to expand the search space and explore new areas for the last N populations, thereby improving the diversity and quality of the initial population.

[0076] 2.5) In the process of reducing the peak factor of multi-frequency sinusoidal excitation signal using the enhanced hippo optimization algorithm, a candidate population set of size 2N is first constructed. The fitness function is designed with "minimizing the peak factor of multi-frequency sinusoidal excitation signal" as the objective function, and the fitness value of each candidate population is calculated. Then, the top N populations with the best fitness values ​​are selected and used as the initial population for optimization in the algorithm iteration process. The algorithm is driven by the initial population to complete the subsequent iteration calculations, and finally the peak factor of multi-frequency sinusoidal excitation signal is effectively reduced.

[0077] 2.6) In the later stages of algorithm iteration, an adaptive t-distribution perturbation strategy is used to escape the local optimum of the algorithm, recalculate the fitness value, and compare it with the previous fitness value to retain the best individual;

[0078] 2.7) Determine if the algorithm has reached the maximum number of iterations. If it has, exit the loop, output the optimal phase, and calculate the optimized multi-frequency sinusoidal excitation signal.

[0079] 3) The charge amplifier 9 converts the charge signal generated by the reference accelerometer 6 into a voltage signal; the data acquisition card 8 simultaneously acquires the voltage signals output by the charge amplifier 9 and the accelerometer 7 to be calibrated, and then transmits them to the data processing and display unit 1;

[0080] 4) Data processing and display unit 1 is based on, for example... Figure 3 The five-parameter sinusoidal approximation method shown above is used to fit the voltage signal acquired by the data acquisition card 8 above, and the frequency, amplitude and phase of each frequency point are calculated.

[0081] The method is as follows:

[0082] 4.1) Define a five-parameter sinusoidal approximation fitting algorithm model to fit the voltage signals output by the charge amplifier 9 and the accelerometer 7 to be calibrated, acquired through the data acquisition card 8, and extract the amplitude and phase at each frequency, as shown in the following formula:

[0083]

[0084] Where y(t) is the fitted voltage signal, used to fit the discrete data acquired by data acquisition card 8 into a continuous function, facilitating signal feature analysis; A i and B i These are the sinusoidal components of the voltage signals output by charge amplifier 9 and accelerometer 7 to be calibrated, respectively; ω iC is the angular frequency; D is the corresponding linear interference component; and C is the corresponding offset component.

[0085] 4.2) Since the voltage signal acquired by data acquisition card 8 contains a small DC bias that is a trend term, it must be removed to obtain the desired trend-term removed signal y1(t). The trend term in the above five-parameter sinusoidal approximation fitting algorithm model is removed using the linear regression method. The mathematical model of the trend term is as follows:

[0086] y trend (t)=C0t+D0(6)

[0087] Solving for C0 and D0 using the least squares method, the signal after removing the trend term is as follows:

[0088] y1(t)=y(t)-(C0t+D0)(7)

[0089] Where C0 and D0 are the initialization parameters of the trend term at the start of nonlinear fitting;

[0090] 4.3) Perform a Fast Fourier Transform (FFT) on the signal y1(t) after removing the trend term to obtain the FFT spectrum. Select the frequencies corresponding to the first K local maxima to estimate the angular frequency and sine and cosine initialization parameters without the trend term.

[0091] 4.4) After analyzing the FFT spectrum to obtain the initial guess parameters, the five-parameter sinusoidal approximation fitting algorithm model after removing the trend term is optimized to minimize the sum of squared residuals between the model output and the measured data. The residual function is defined as follows:

[0092]

[0093] Where, θ=[A i B i ,ω i [C,D] represents the parameter vector to be optimized, M is the time series length, and t... m These are actual measured data;

[0094] 4.5) Iteratively update the parameters to be optimized using the Levenberg-Marquardt (LM) algorithm, as shown in the following formula:

[0095] θ (iter+1) =θ (iter) -(J T J+λI) -1 J T r(θ (iter) (9)

[0096] Where J is the Jacobian matrix of the residuals with respect to the parameters; r is the residual vector; λ is the damping factor used to control the iteration step size; iter is the current iteration number;

[0097] 4.6) After obtaining the optimal value of each parameter to be optimized, a continuous signal is generated as follows:

[0098]

[0099] in, and These represent the amplitude, angular frequency, and initial phase of the sinusoidal component at the i-th frequency point, respectively.

[0100] 5) Based on the frequency, amplitude and phase of each of the above frequency points, the data processing and display unit 1 calculates the amplitude sensitivity and phase sensitivity of the accelerometer 7 to be calibrated at each of the above frequency points using a comparison method, thereby completing one calibration.

[0101] Since the amplitude sensitivity of the reference accelerometer 6 is known, its output reflects the true acceleration amplitude and phase information of the intermediate frequency standard vibration table 4 at that frequency point; the amplitude sensitivity of the accelerometer 7 to be calibrated is unknown, and its output is the corresponding voltage signal. Using a comparison method, the amplitude and phase of the reference accelerometer 6 and the accelerometer 7 to be calibrated are compared at the same frequency point. The amplitude difference and phase difference collected by the reference accelerometer 6 and the accelerometer 7 to be calibrated at the same frequency point are defined as the amplitude sensitivity and phase sensitivity of the accelerometer 7 to be calibrated, respectively, thus completing the calibration of the entire frequency band in one go.

[0102] To verify the calibration accuracy of the method of the present invention, the inventors used the data processing and display unit 1 to superimpose 14 single-frequency sine components with an amplitude of 0.2V in the frequency range of 50-1000Hz. Then, the signal was output through the signal generator 2 and acquired by the data acquisition card 8. Finally, the five-parameter sine approximation algorithm proposed in this invention was used to fit the data. The specific data fitting results are shown in Table 1. Figure 5 The figure shows the fitting result of the voltage signal output by signal generator 2 in this embodiment of the invention. The measurement data shows that the absolute relative deviation of the frequency fitting and the absolute relative deviation of the amplitude fitting are 0.0009% and 0.3%, respectively. This indicates that the method of the present invention has high accuracy for fitting multi-frequency sinusoidal excitation signals.

[0103] Table 1. Fitting results of the superposition of 14 single-frequency sinusoidal components between 50-1000Hz

[0104]

[0105] In addition, tests were conducted within the frequency range of 39-3163Hz. Using the logarithmic interval frequency distribution method, 21 frequency points were selected for accelerometer sensitivity calibration experiments. The calibration results are as follows: Figure 6-7 As shown in the figure. Experimental results confirm that this method greatly improves calibration efficiency while ensuring calibration accuracy.

Claims

1. A method for dynamic sensitivity calibration of an ultra-efficient accelerometer based on multi-frequency sinusoidal excitation, characterized in that: The ultra-efficient accelerometer sensitivity dynamic calibration method based on multi-frequency sinusoidal excitation includes the following steps performed in sequence: 1) Construct a broadband accelerometer sensitivity calibration system, which includes a data processing and display unit (1), a signal generator (2), a power amplifier (3), an intermediate frequency standard vibration table (4), a reference accelerometer (6), an accelerometer to be calibrated (7), a data acquisition card (8), and a charge amplifier (9); wherein, the upper end of the intermediate frequency standard vibration table (4) is provided with a work surface (5); the accelerometer to be calibrated (7) and the reference accelerometer (6) are fixed on the work surface (5) from top to bottom; the data processing and display unit (1) is electrically connected to the intermediate frequency standard vibration table (4) in sequence through the signal generator (2) and the power amplifier (3); the data acquisition card (8) is electrically connected to the reference accelerometer (6) through the charge amplifier (9), and is also electrically connected to the accelerometer to be calibrated (7) and the data processing and display unit (1); 2) The data processing and display unit (1) optimizes the multi-frequency sinusoidal excitation signal based on the logarithmic interval frequency distribution method and the enhanced hippo optimization algorithm, and controls the signal generator (2) to output the optimized multi-frequency sinusoidal excitation signal. Then, the power amplifier (3) amplifies the signal and drives the worktable (5) on the intermediate frequency standard vibration table (4) to generate multi-frequency sinusoidal vibration. At the same time, the accelerometer to be calibrated (7) and the reference accelerometer (6) maintain the same motion characteristics as the worktable (5). 3) The charge amplifier (9) converts the charge signal generated by the reference accelerometer (6) into a voltage signal; the data acquisition card (8) simultaneously acquires the voltage signals output by the charge amplifier (9) and the accelerometer (7) to be calibrated, and then transmits them to the data processing and display unit (1); 4) Data processing and display unit (1) fits the voltage signal acquired by the above data acquisition card (8) based on the five-parameter sinusoidal approximation method, and calculates the frequency, amplitude and phase of each frequency point; 5) The data processing and display unit (1) calculates the amplitude sensitivity and phase sensitivity of the accelerometer (7) to be calibrated at each of the above frequency points based on the frequency, amplitude and phase of each of the above frequency points using the comparison method, thereby completing a calibration.

2. The method for dynamic sensitivity calibration of an ultra-efficient accelerometer based on multi-frequency sinusoidal excitation according to claim 1, characterized in that: In step 2), the data processing and display unit (1) optimizes the multi-frequency sinusoidal excitation signal based on the logarithmic interval frequency distribution method and the enhanced hippo optimization algorithm as follows: 2.1) The logarithmic interval frequency distribution method is used to effectively suppress harmonic interference from multi-frequency sinusoidal excitation signals. The calculation formula is as follows: Among them, f i Let be the frequency value of the i-th single-frequency sinusoidal component in the multi-frequency sinusoidal excitation signal, and K be the total number of single-frequency sinusoidal components that make up the multi-frequency sinusoidal excitation signal; 2.2) Define the signal crest factor as the ratio of the peak value to the RMS value of the time-domain signal: Among them, V pk V represents the peak value of the time-domain signal. rms The effective value of the time-domain signal; 2.3) Set the population size N and the maximum number of iterations T for the enhanced hippo optimization algorithm. max The population position is initialized using random numbers in the interval (0,1), as shown in the following expression: Y j =lb j +ο1·(ub j -lb j )(3) Where ο1 is an N×1 vector of random numbers, where each element is uniformly distributed between 0 and 1, and ub j and lb j These are the upper and lower bounds of the search space for each dimension, respectively; N is the population size; and m is the number of dimensions in the problem. The initial population position matrix is ​​represented as follows: 2.4) Increase the population size N to 2N, use Latin hypercube sampling to evenly distribute the first N populations, and use adaptive lens back learning to expand the search space and explore new areas for the last N populations, thereby improving the diversity and quality of the initial population. 2.5) In the process of reducing the peak factor of multi-frequency sinusoidal excitation signal using the enhanced hippo optimization algorithm, a candidate population set of size 2N is first constructed. The fitness function is designed with "minimizing the peak factor of multi-frequency sinusoidal excitation signal" as the objective function, and the fitness value of each candidate population is calculated. Then, the top N populations with the best fitness values ​​are selected and used as the initial population for optimization in the algorithm iteration process. The algorithm is driven by the initial population to complete the subsequent iteration calculations, and finally the peak factor of multi-frequency sinusoidal excitation signal is effectively reduced. 2.6) In the later stages of algorithm iteration, an adaptive t-distribution perturbation strategy is used to escape the local optimum of the algorithm, recalculate the fitness value, and compare it with the previous fitness value to retain the best individual; 2.7) Determine if the algorithm has reached the maximum number of iterations. If it has, exit the loop, output the optimal phase, and calculate the optimized multi-frequency sinusoidal excitation signal.

3. The method for dynamic sensitivity calibration of an ultra-efficient accelerometer based on multi-frequency sinusoidal excitation according to claim 1, characterized in that: In step 4), the data processing and display unit (1) uses a five-parameter sine approximation method to fit the voltage signal acquired by the data acquisition card (8) and calculates the frequency, amplitude, and phase of each frequency point as follows: 4.1) Define a five-parameter sinusoidal approximation fitting algorithm model to fit the voltage signals output by the charge amplifier (9) and the accelerometer (7) to be calibrated, obtained through the data acquisition card (8), and extract the amplitude and phase at each frequency, as shown in the following formula: Where y(t) is the fitted voltage signal, used to fit the discrete data acquired by the data acquisition card (8) into a continuous function, facilitating signal feature analysis; A i and B i These are the sinusoidal components of the voltage signals output by the charge amplifier (9) and the accelerometer to be calibrated (7), respectively; ω i C is the angular frequency; D is the corresponding linear interference component; and C is the corresponding offset component. 4.2) The trend term in the five-parameter sinusoidal approximation fitting algorithm model above is removed using the linear regression method. The mathematical model of the trend term is as follows: y trend (t)=C0t+D0(6) Solving for C0 and D0 using the least squares method, the signal after removing the trend term is as follows: y1(t)=y(t)-(C0t+D0)(7) Where C0 and D0 are the initialization parameters of the trend term at the start of nonlinear fitting; 4.3) Perform a Fast Fourier Transform on the signal y1(t) after removing the trend term to obtain the FFT spectrum. Select the frequencies corresponding to the first K local maxima to estimate the angular frequency and sine and cosine initialization parameters without the trend term. 4.4) After analyzing the FFT spectrum to obtain the initial guess parameters, the five-parameter sinusoidal approximation fitting algorithm model after removing the trend term is optimized to minimize the sum of squared residuals between the model output and the measured data. The residual function is defined as follows: Where, θ=[A i B i ,ω i [C,D] represents the parameter vector to be optimized, M is the time series length, and t... m These are actual measured data; 4.5) Iteratively update the parameters to be optimized using the Levenberg-Marquardt algorithm, as shown in the following formula: i (iter+1) =θ (iter) -(J T J+λI) -1 J T r(θ (iter) (9) Where J is the Jacobian matrix of the residuals with respect to the parameters; r is the residual vector; λ is the damping factor used to control the iteration step size; iter is the current iteration number; 4.6) After obtaining the optimal value of each parameter to be optimized, a continuous signal is generated as follows: in, and These represent the amplitude, angular frequency, and initial phase of the sinusoidal component at the i-th frequency point, respectively.

4. The method for dynamic sensitivity calibration of an ultra-efficient accelerometer based on multi-frequency sinusoidal excitation according to claim 1, characterized in that: In step 5), the data processing and display unit (1) calculates the amplitude sensitivity and phase sensitivity of the accelerometer (7) to be calibrated at each of the above frequency points based on the frequency, amplitude, and phase of each frequency point using a comparison method. The method for completing one calibration is as follows: The amplitude sensitivity of the reference accelerometer (6) is known, while the amplitude sensitivity of the accelerometer to be calibrated (7) is unknown. Using a comparison method, the amplitude and phase of the reference accelerometer (6) and the accelerometer to be calibrated (7) at the same frequency point are compared. The amplitude difference and phase difference collected by the reference accelerometer (6) and the accelerometer to be calibrated (7) at the same frequency point are defined as the amplitude sensitivity and phase sensitivity of the accelerometer to be calibrated (7), thereby completing the calibration of the entire frequency band in one go.

Images