A decoupling method for triaxial accelerometer based on surface fitting and time-frequency analysis

Abstract

The present invention discloses a decoupling method of a three-axis accelerometer based on surface fitting and time-frequency analysis, comprising the following steps: obtaining calibration data of the accelerometer, the calibration data is input and output data obtained under different vibration frequencies of an excitation platform with one axis of the accelerometer as input and other axes as output; performing segmented surface fitting according to the calibration data to obtain a coupling function between the axes with vibration frequency and vibration amplitude as input and coupling amplitude as output; performing time-frequency analysis on an unknown signal using continuous wavelet transform to obtain the frequency of the signal; bringing the vibration amplitude and vibration frequency of the unknown signal into the coupling function to obtain the coupling amplitude; for any axis, obtaining the output after removing the inter-dimensional coupling according to the formula as the calibrated output. The present invention improves the real-time performance of decoupling, greatly reduces the amount of calculation required for decoupling, has good versatility, and effectively improves the measurement accuracy of the sensor.

Description

Technical Field

[0001] The invention relates to the field of multidimensional accelerometer signal processing, and in particular to a three-axis accelerometer decoupling method based on surface fitting and time-frequency analysis. Background Art

[0002] Three-dimensional acceleration sensors have been widely used in many fields such as inertial measurement of aircraft, robot balance detection, limb posture detection, and seismic detection. When there is mutual influence between different axial sensitive elements of the sensor, inter-dimensional coupling will occur between multi-dimensional signals during the measurement process, which limits the measurement accuracy of the multi-dimensional acceleration sensor. For example, in the field of seismic exploration, three-dimensional acceleration seismic detectors are widely used. When these detectors have inter-dimensional coupling interference, the seismic wave signals they receive will introduce errors or even produce distortion. At the same time, in the process of seismic exploration, a large number of seismic detectors are deployed, such as thousands or even tens of thousands. Together, they form a distributed control system and use embedded systems to realize data acquisition. When using decoupling algorithms to reduce or eliminate the inter-dimensional coupling interference of these seismic detectors, the best way is to implement decoupling in each embedded system, that is, distributed modular decoupling, which can significantly improve the decoupling real-time performance and the working efficiency of the entire system while ensuring the decoupling accuracy. With the continuous improvement of the measurement accuracy requirements of three-dimensional acceleration sensors in different fields, more and more application scenarios require inter-dimensional coupling decoupling and modular decoupling.

[0003] The decoupling method using sensor input and output data and analyzing calibration data is the general trend of decoupling research. Its advantage is that it does not require knowing the transfer function of the sensor. However, most of the existing decoupling methods require iteration, large amount of calculation, and are only suitable for PCs, not suitable for porting to decoupling modules. At the same time, the decoupling methods of multi-dimensional force / torque sensors have been widely studied, but there are few reports on the decoupling research of multi-dimensional acceleration sensors. Unlike multi-dimensional force / torque sensors with a single input variable, the input variables of multi-dimensional acceleration sensors include vibration frequency and vibration acceleration, and their inter-dimensional coupling function changes from two-dimensional to three-dimensional, which brings new challenges to inter-dimensional coupling decoupling.

[0004] Most of the existing decoupling methods only process data on the PC side. In order to realize real-time dynamic decoupling, the present invention chooses to perform decoupling in an embedded system. However, it is found in the implementation process that the frequency of the unknown signal cannot be directly obtained. Therefore, time-frequency analysis is used to obtain the frequency of the signal at each moment, and the time-amplitude-frequency of the signal is obtained. At the same time, the present invention improves the segmentation method of fitting, and adopts the method of calculating the maximum point of the curve for segmentation, which reduces the calculation amount and calculation time of segmentation fitting. On the basis of decoupling in an embedded system, the present invention introduces a time-frequency analysis method, which can obtain the amplitude and frequency of the signal that change with time, and realizes real-time dynamic decoupling; improves the segmentation method of fitting, and improves the segmentation efficiency; the proposed decoupling method can meet any multi-dimensional sensor, and effectively improves the sensor measurement accuracy. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a three-axis accelerometer decoupling method based on surface fitting and time-frequency analysis, and the method comprises the following steps:

[0006] S1. Obtain calibration data of the accelerometer, where the calibration data is input and output data obtained at different vibration frequencies of the vibration table with one axis of the accelerometer as input and other axes as output;

[0007] S2: Perform segmented surface fitting based on the calibration data to obtain the coupling function between the axes, with the vibration frequency and vibration amplitude as input and the coupling amplitude as output;

[0008] S3: Use continuous wavelet transform to perform time-frequency analysis on the unknown signal to obtain the frequency of the signal;

[0009] S4: Substitute the vibration amplitude and vibration frequency of the unknown signal into the coupling function to obtain the coupling amplitude;

[0010] S5: For any axial direction, the output after removing the inter-dimensional coupling is obtained according to the formula as the calibrated output.

[0011] The beneficial effects provided by the present invention are as follows: the proposed decoupling method is based on fitting and solving the coupling model, while avoiding the tedious iterative solution of the coupling relationship, using a clear function to characterize the coupling relationship between the dimensions of the acceleration sensor, improving the real-time performance of the decoupling, and greatly reducing the amount of calculation required for the decoupling. It is very suitable for low-cost, low-calculation embedded systems, such as digital signal processing chips. On the basis of decoupling the embedded system, a time-frequency analysis method is introduced to obtain the amplitude and frequency of the signal changing with time, and real-time dynamic decoupling is realized. The proposed decoupling method can be applied to any multidimensional sensor, has good versatility, and effectively improves the sensor measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a schematic flow chart of the method of the present invention;

[0013] Figure 2 is a schematic diagram of the calibration equipment;

[0014] Figure 3 is the coupling model obtained by fitting;

[0015] Figure 4 Here is the original signal and its time-frequency diagram:

[0016] Figure 4 (a) is the original acceleration signal; Figure 4 (b) is the wavelet time-frequency diagram;

[0017] Figure 5 It is a comparison chart of coupling values ​​before and after decoupling. DETAILED DESCRIPTION

[0018] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0019] Please refer to Figure 1 , Figure 1 The present invention is a flow chart of a method; a triaxial accelerometer decoupling method based on surface fitting and time-frequency analysis, the method comprising the following steps:

[0020] S1. Obtain calibration data of the accelerometer, where the calibration data is input and output data obtained at different vibration frequencies of the vibration table with one axis of the accelerometer as input and other axes as output;

[0021] It should be noted that the accelerometer is a three-axis MEMS acceleration sensor, or one of three-axis accelerometers such as a multi-dimensional acceleration sensor, a multi-dimensional torque sensor, a multi-dimensional wheel force sensor, and a multi-dimensional flexible tactile sensor;

[0022] Please refer to Figure 2 , Figure 2 is a schematic diagram of the vibration table and calibration data acquisition equipment; the calibration data obtained according to the equipment is shown in Table 1;

[0023] Table 1 Part of the calibration data

[0024]

[0025] All input and output data sets are processed in order from small to large according to the vibration frequency f. During the segmented fitting process, each segment is fitted using the least squares method.

[0026] S2: Perform segmented surface fitting based on the calibration data to obtain the coupling function between the axes, with the vibration frequency and vibration amplitude as input and the coupling amplitude as output; please refer to Figure 3 , Figure 3 This is the obtained coupling model;

[0027] It should be noted that in step S2, the input and output data obtained in step 1 are used for fitting to obtain the fitted coefficient P 1，1 , P 2，1 ,…P n,n-1 To obtain the inter-dimensional coupling function expression:

[0028]

[0029] In the formula, a≠b, variable f is the frequency, and variable u is a is the non-dimensional coupling output, k and x are the highest order during fitting and are positive integers.

[0030] It should be noted that in step S2, the specific process of piecewise surface fitting is:

[0031] S21, determining the highest order of the coupling function input variables vibration frequency f and vibration amplitude u;

[0032] S22, taking the vibration frequency f as input and the coupling amplitude z as output, fitting to obtain a relationship curve between the vibration frequency and the coupling amplitude under a fixed vibration amplitude u;

[0033] S23. Find the maximum point of the curve. The frequency corresponding to the maximum point is the segmentation point.

[0034] The segmentation method of the present invention needs to first determine the highest order of the coupling function input variables vibration frequency f and vibration amplitude u. After determining the highest order, it is only necessary to calculate and fit the maximum value of the relationship curve between vibration frequency and coupling amplitude under the fixed vibration amplitude u. The frequency corresponding to the maximum point is the segmentation point. There is no need to calculate the fitting determination coefficient and fitting standard deviation of each set of data. The calculation amount of the segmentation process is smaller and the calculation time is shorter, but the final segmentation result is the same as the above patent. After fitting the curve, the segmentation points of the surface can also be roughly estimated based on the maximum points shown in the image.

[0035] S3: Use continuous wavelet transform to perform time-frequency analysis on the unknown signal to obtain the frequency of the signal;

[0036] It should be noted that in step 3, time-frequency analysis is applied to decoupling. The decoupling of multi-dimensional acceleration sensor data has an additional important variable, frequency, compared to the decoupling of multi-dimensional force / torque sensors. However, the acceleration signal collected by the ADC is a time domain signal, and the frequency cannot be directly obtained. Please refer to Figure 4(a), the amplitude corresponding to time is known, but the frequency corresponding to time is unknown. Time-frequency analysis is a tool to obtain the frequency corresponding to time. The unknown signal refers to the time-amplitude signal acquired by ADC. In order to achieve real-time decoupling, the present invention uses complex morlet continuous wavelet transform to perform time-frequency analysis on the unknown signal to obtain the frequency corresponding to time. Please refer to Figure 4 (b). In the complex morlet wavelet transform, the mother wavelet (wavelet basis function) is a single-frequency complex sine function under a Gaussian envelope, where the complex trigonometric function corresponds to the frequency, and the exponentially decaying Gaussian function corresponds to the finite support of the function in the time domain. The wavelet basis function formula is as follows:

[0037] φ(z)=exp(-t2 / 2)*exp(jw0t)

[0038] Scaling and translating the wavelet basis function:

[0039] φ a,b (z)=1 / a*exp[-(tb)2 / 2a2]*exp[jw0(tb) / a]

[0040] Among them, a is the scale factor. By changing the size of a (scaling transformation), the wavelet function is scaled. The larger the scale factor a is, the lower the function center frequency is, the slower the function exponential decay is, the larger the time domain support interval is, the smaller the frequency domain bandwidth is, and the higher the frequency domain resolution is. When a is smaller, the change is the opposite. The time shift factor b realizes the translation of the wavelet function on the coordinate axis.

[0041] It should be noted that, in some other embodiments, the time-frequency analysis method may be continuous wavelet transform, short-time Fourier transform, S transform, Wigner-Ville distribution, empirical mode decomposition, synchronous compression wavelet transform, etc.

[0042] It should be noted that

[0043] S4: Substitute the vibration amplitude and vibration frequency of the unknown signal into the coupling function to obtain the coupling amplitude;

[0044] S5: For any axial direction, the output after removing the inter-dimensional coupling is obtained according to the formula as the calibrated output.

[0045] In steps S4 and S5, the vibration amplitude of the unknown signal collected and the vibration frequency obtained by time-frequency analysis are substituted into the coupling function expression obtained by segmented surface fitting in step 2, the coupling value is calculated, the coupling value is removed, and the output after removing the inter-dimensional coupling in the axial direction is obtained as the calibrated output. The coupling values ​​before and after decoupling are compared. Figure 5 As shown, acce_z is the vibration amplitude, coup_y is the y-axis coupling amplitude, and Method is the y-axis amplitude after decoupling.

[0046] The beneficial effects of the present invention are as follows: the proposed decoupling method is based on fitting and solving the coupling model. While avoiding the tedious iterative solution of the coupling relationship, it uses a clear function to characterize the coupling relationship between the dimensions of the acceleration sensor, improves the real-time performance of the decoupling, and greatly reduces the amount of calculation required for the decoupling. It is very suitable for low-cost, low-calculation embedded systems, such as digital signal processing chips. On the basis of decoupling the embedded system, a time-frequency analysis method is introduced to obtain the amplitude and frequency of the signal changing with time, thereby realizing real-time dynamic decoupling. The proposed decoupling method can be applied to any multidimensional sensor, has good versatility, and effectively improves the sensor measurement accuracy.

[0047] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A three-axis accelerometer decoupling method based on surface fitting and time-frequency analysis, characterized in that: The following steps are involved: S1. Obtain calibration data of the accelerometer, where the calibration data is input and output data obtained at different vibration frequencies of the vibration table with one axis of the accelerometer as input and other axes as output; S2: Perform segmented surface fitting based on the calibration data to obtain the coupling function between the axes, with the vibration frequency and vibration amplitude as input and the coupling amplitude as output; In step S2, the input and output data obtained in step S1 are used for fitting to obtain the fitted coefficient P 1，1 , P 2，1 ,…P n,n-1 To obtain the inter-dimensional coupling function expression: In the formula, a≠b, variable f is the frequency, and variable u is a is the non-dimensional coupling output, k and x are the highest order during fitting and are positive integers; In step S2, the specific process of piecewise surface fitting is as follows: S21, determining the highest order of the coupling function input variables vibration frequency f and vibration amplitude u; S22, taking the vibration frequency f as input and the coupling amplitude z as output, fitting to obtain a relationship curve between the vibration frequency and the coupling amplitude under a fixed vibration amplitude u; S23, solving the maximum point of the curve, the frequency corresponding to the maximum point is the segmentation point; S3: Use continuous wavelet transform to perform time-frequency analysis on the unknown signal to obtain the frequency of the signal; S4: Substitute the vibration amplitude and vibration frequency of the unknown signal into the coupling function to obtain the coupling amplitude; S5: For any axial direction, the output after removing the inter-dimensional coupling is obtained according to the formula as the calibrated output; In steps S4 and S5, the vibration amplitude of the collected unknown signal and the vibration frequency obtained by time-frequency analysis are substituted into the coupling function expression obtained by segmented surface fitting in step S2 to calculate the coupling value, remove the coupling value, and obtain the output after removing the inter-dimensional coupling in the axial direction as the calibrated output.

2. A three-axis accelerometer decoupling method based on surface fitting and time-frequency analysis as claimed in claim 1, characterized in that: In step S3, complex morlet continuous wavelet transform is used to perform time-frequency analysis on the unknown signal to obtain the frequency corresponding to the time.

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