CN113777350A - Acceleration sensor data processing method based on stabilized numerical integration - Google Patents
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Abstract
The invention discloses an acceleration sensor data processing method based on stabilized numerical integration. Firstly, carrying out Kalman filtering and acceleration sensor parameter calibration on acquired acceleration sensor raw data; then, correcting a transfer function of the acceleration integral critical stabilization system by adopting a Simpson method based on stabilization numerical integration to construct a stabilization integration system; and finally, carrying out primary integration on the preprocessed acceleration sensor data by using the constructed stabilization integration system to obtain speed, carrying out secondary integration to obtain displacement, and carrying out error analysis on an integration result by using an acceleration integration error evaluation index. The method improves the traditional numerical integration method based on the Simpson method, and can effectively inhibit result drift generated by multiple integration of acceleration data by utilizing the self characteristics of a stable system.
Description
Technical Field
The invention belongs to the technical field of sensor signal detection and data processing, and particularly relates to an acceleration sensor data processing method based on stabilization numerical integration.
Background
The acceleration sensor has high reliability and wide measurable frequency band, can be directly and rigidly connected with the structure to be measured, and the installation position does not need to be static relative to the structure to be measured. Compared with the direct speed and displacement test, the acceleration is measured and then integrated to obtain the speed and the displacement, so that the speed and the displacement are simpler and more convenient. Therefore, the measurement of speed and displacement information by using an acceleration sensor is widely applied to military and civil engineering practices, for example, in the military field, muzzle vibration acceleration is measured by using an acceleration sensor in a contact manner when a gun is fired, and muzzle vibration displacement is obtained by integration (li shi li, guo 26107, ducman, and so on. image processing based on the precision of the high sub-pixel measures tank muzzle vibration displacement [ J ]. proceedings of testing technology, 2017 (2)); in the civil field, firstly, the vibration acceleration of a bridge point to be measured is obtained through different excitation modes such as dynamic non-dynamic, continuous and discontinuous, single-point and multi-point and the like, and then, the vibration displacement signal of the bridge is obtained by carrying out secondary integration on the acceleration signal (a standard art silk, Zhaowei steel, bridge dynamic displacement test digital processing method research [ J ]. national defense traffic engineering and technology, 2011(01): 15-18.).
The acceleration sensor data usually contains components such as zero offset, installation error, Gaussian random noise and the like, and due to the existence of the trend terms, the accumulated error is increased continuously by directly integrating the acceleration data, and the secondary integration result of the acceleration data can generate severe drift. Therefore, when integrating the acceleration data, the trend term needs to be processed to reduce its influence on the integration result. The currently commonly used acceleration data integration methods include a time domain numerical integration method (a moving displacement monitoring method based on a real-time acceleration integration algorithm of a recursive least square method, such as a midpoint rectangle method, a trapezoid method, a Simpson method, a least square method and the like (Danshin, Zhengwenha, Yanxinwu, Yanxinfei, a non-zero) and a moving displacement monitoring method of a real-time acceleration integration algorithm based on the recursive least square method, a Zhongjie acceleration test integration displacement algorithm and application thereof to research [ D ]. Chongqing university, 2013.), and a spatial domain method (consider Weidong, Luxin, FIR digital filtering in an MEMS accelerometer and application thereof [ J ]. micro-nano electronic technology, 2009,046, (735) and 738, Xinxin, Scyu, WieslawJ.Staszekki, and the like, 2012,31(020), 166-171; li Huihao, Xibaojie, Zuoyunwan, etc. based on wavelet transform and EMD method extraction trend item contrast research [ J ] instrument, meter and analysis monitoring, 2013(03):28-30 ].
However, the poles of the transfer function of the conventional numerical integration system are on the unit circle, which constitutes a critically stable system, and the acceleration signal with disturbance is integrated, and the result is divergent. In actual measurement, because external interference signals exist and cannot be effectively eliminated, the processed acceleration data still has flaws or micro drift, and the precision of speed and displacement values obtained after the acceleration data is integrated needs to be improved. In 2014, Nanjing, university of Engineers, Xiaochong and the like apply a stabilization numerical integration method to the solution of the shock wave pressure specific impulse to obtain more accurate specific impulse of the detonation shock wave explosion of the cloud bomb (Xiaodao, Konderen, Lilismna, and the like.) of the shock wave pressure specific impulse solving method discussion [ J ] of the missile and rocket and guidance bulletin, 2014,34(005): 94-97.). However, the application of the stabilization numerical integration method in the acceleration integration is still less studied. Therefore, it is necessary to find an appropriate integration method to obtain an accurate integral value and to improve the calculation accuracy of the velocity and the displacement.
Disclosure of Invention
The invention aims to provide an acceleration sensor data processing method based on stabilized numerical integration, which effectively corrects a critical stable integral system of a traditional numerical function to construct a stable integral system, overcomes the problem that an integral result obtained by utilizing the traditional numerical integration is drifted, improves the precision of the acceleration integral result and has feasibility in engineering practice.
The technical scheme for realizing the aim of the invention is that the invention provides an acceleration sensor data processing method based on stabilized numerical integration, which comprises the following steps:
(10) acceleration data acquisition: statically placing an acceleration sensor on a working platform, and collecting acceleration original data output by three shafts of the acceleration sensor within a period of time;
(20) preprocessing raw data: filtering the acquired acceleration original data by adopting a Kalman filtering algorithm to obtain filtered acceleration data;
(30) calibrating parameters of an acceleration sensor: establishing an error model of the acceleration sensor, and calibrating parameters of the acceleration sensor by adopting a six-position method;
(40) integration of acceleration data: performing primary integration on acceleration sensor data by adopting an acceleration sensor data processing method based on stabilization numerical integration to obtain speed; integrating the speed for the first time to obtain displacement;
(50) and (3) integral error analysis: and evaluating an acceleration integral error by adopting a peak error, a difference error and an absolute error.
The (10) acceleration data acquisition step includes:
(11) statically placing an acceleration sensor on a horizontal workbench, wherein the sampling frequency of the used acceleration sensor is 200 Hz;
(12) the acceleration sensor is connected with a computer through a data line;
(13) setting the data acquisition time to be 1 minute, and adopting data acquisition software to acquire data.
The parameter calibration of the acceleration sensor (30) is mainly carried out by adopting a six-position method, and the method comprises the following specific steps:
(31) constructing an error model of the acceleration sensor: an acceleration sensor error model is constructed according to the formula (1):
formula (1), (A)x,Ay,Az]TThe actual measured value is the actual measured value of the acceleration sensor; [ a ] Ax,ay,az]TIs the true value; [ a ] Ax0,ay0,az0]TZero bias in g; kx1,Ky1,Kz1,Kx2,Ky2,Kz2Is a mounting error coefficient; sx,Sy,SzIs a scale factor.
(32) The acceleration sensor is statically placed on a horizontal workbench by adopting a six-position method, and each position is placed for 1 minute;
(33) respectively collecting output data (A) of each axis of the acceleration sensor at each positionxi,Ayi,Azi),i＝1,...,6；
(34) Calibrating parameters of an acceleration sensor: calibrating the parameters of the acceleration sensor according to the formula (2) to obtain the zero offset [ a ] of the acceleration sensorx0,ay0,az0]TMounting error Kx1,Ky1,Kz1,Kx2,Ky2,Kz2And scale factor Sx,Sy,Sz：
The (40) acceleration data integrating step includes:
(41) transfer function modification: modifying a transfer function of an integral system of a Simpson numerical integration algorithm according to an equation (5) to construct a stable integral system:
equation (5), X (z) is the z-transform of a time-continuous function x (t), Y (z) is the z-transform of the time-continuous function x (t) integrating the results over the sample interval [0, KT ]; h (z) is the transfer function of the integral system; t is a sampling interval; c is a stability factor for stabilizing the integration system.
(42) First integration: the acceleration sensor data is integrated once according to equation (6), and the obtained velocity can be expressed as:
formula (6), a (n) is acceleration data; v (n) is velocity data; t is a sampling interval; c is a correction factor for a stable integration system.
(43) Second integration: the displacement is obtained by integrating the velocity again according to equation (7). The displacements obtained by reintegrating the velocity shown in equation (6) by the stabilization integration system constructed by the stabilization simpson method shown in equation (5) can be respectively expressed as:
formula (3), v (n) is velocity; s (n) is a displacement; t is a sampling interval; c is a stability factor for stabilizing the integration system.
The (50) integrating error analyzing step includes:
(51) evaluating the error of the acceleration integration result according to the peak error, the difference error and the absolute error shown in the formulas (8) to (10):
the difference error err _ diff represents the average of the integrated result peak and the true peak error, i.e.:
the absolute error err _ abs represents the ratio of the difference between the integration result and the true value to the true value, i.e.:
the expressions (8) to (10), s (t) being the integration result; st(t) is true.
(52) The peak error, the difference error and the absolute error of the integration result of the method are compared with those of the integration result of the traditional Simpson method.
Compared with the prior art, the invention has the remarkable advantages that: the method applies a stabilized numerical integration method to the traditional acceleration integration based on the Simpson method, constructs a stable system by correcting the transfer function of a critical stable integration system under a z-transformation frame, effectively inhibits the drift of an integration result by utilizing the characteristics of the stable system, and obtains more accurate speed and displacement results.
Drawings
Fig. 1 is a flow chart of a data processing method of an acceleration sensor based on stabilization numerical integration according to the present invention.
FIG. 2 shows an acceleration sensor coordinate system O-XYZ and a measurement coordinate system O-XYZ.
FIG. 3 is a schematic diagram of the Simpson numerical integration method and the distribution of the poles of the integration system. (a) The simpson method and (b) the pole distribution of the simpson method.
Fig. 4 is a schematic diagram of an acceleration sensor data acquisition system.
Detailed Description
The invention provides an acceleration sensor data processing method based on stabilized numerical integration, which has the following basic ideas:
firstly, preprocessing acquired raw data of the acceleration sensor, wherein the processing method comprises Kalman filtering and acceleration sensor parameter calibration;
then, correcting the traditional acceleration integral critical stabilization system by adopting a Simpson method based on stabilization numerical integration to construct a stabilization integration system;
and finally, carrying out primary integration on the preprocessed acceleration sensor data by using the constructed stabilization integration system to obtain speed, carrying out secondary integration to obtain displacement, and carrying out error analysis on an integration result by using an acceleration integration error evaluation index.
Acceleration sensor data preprocessing
The acceleration sensor is one of the core devices of the inertial measurement unit, and the zero offset, the scale factor and the installation error of the acceleration sensor are main errors influencing the precision. As shown in FIG. 2, O-XYZ is the acceleration sensor coordinate system and O-XYZ is the measurement coordinate system. When the device is installed, all axes of the acceleration sensor and all axes of the measuring coordinate system are not completely overlapped, so that the sensor coordinate system and the measuring coordinate system have deviation. While a zero bias error causes the integration initial value to be non-zero and produces an accumulated error. Therefore, a correlation error model is required to be established, and the error is compensated and corrected in real time.
1. Error model of acceleration sensor
The acceleration sensor error model can be expressed as:
formula (1), (A)x,Ay,Az]TThe actual measured value is the actual measured value of the acceleration sensor; [ a ] Ax,ay,az]TIs the true value; [ a ] Ax0,ay0,az0]TZero bias in g; kx1,Ky1,Kz1,Kx2,Ky2,Kz2Is a mounting error coefficient; kx3,Ky3,Kz3Is a quadratic error coefficient in g-1；Sx,Sy,SzIs a scale factor; w is ax,wy,wzIs the gaussian noise of the system, which has a mean value of zero and has a uniform probability density and white power spectral density.
2. Kalman filtering
After the acceleration data is obtained, firstly, filtering the original data by adopting a Kalman filtering algorithm to filter [ w ] in the formula (1)x,wy,wz]TComponent to reduce numberAccording to the influence of Gaussian noise generated by a system in acquisition on data.
Kalman filtering is an optimal estimation method based on the minimum error covariance criterion, has small calculated amount and high real-time property, can continuously correct the estimated value of the future motion state by utilizing the actual motion parameters, improves the estimation precision and simultaneously gives consideration to the real-time property and the stability.
The state equations and measurement equations of Kalman filtering can be expressed as:
formula (2), A is a state transition matrix; h is a measurement matrix; w, V are the state and measurement noise matrices, respectively, and are uncorrelated positive and too white noise, and the variances are Q, R, respectively.
The Kalman filtered state vector prediction equation, state vector covariance matrix prediction equation, state vector update equation, state vector covariance update equation, and Kalman gain matrix may be expressed as:
the compound of the formula (3),
is a predicted state;
is a state estimation; pi|i-1Is the prediction error covariance; piEstimating error covariance; kiIs the gain; and I is an identity matrix.
The Kalman filtering method is described in detail in literature (Ali J, Ushaq M.A configuration and robust Kalman filter design for in-motion alignment system [ J ]. Measurement,2009, 42(4): 577-.
3. Six-position calibration method for acceleration sensor
The quadratic error term in equation (1) can be ignored since quadratic errors in engineering applications have less influence on the accuracy of the acceleration sensor. After Kalman filtering, the error model of the acceleration sensor can be simplified as follows:
as can be seen from equation (4), the error model of the acceleration sensor has 12 parameters to be corrected, including zero offset ax0,ay0,az0Mounting error Kx1,Ky1,Kz1,Kx2,Ky2,Kz2And the scale factor Sx,Sy,Sz. The error model coefficients of the acceleration sensor are identified by a classical six-position calibration method, the acceleration sensor to be corrected is placed at six special positions listed in the table 1, so that each coefficient in the model is eliminated, and each parameter in the formula (4) can be obtained.
Table 1 six-position calibration comparison table for acceleration sensor
The six-position calibration method of the acceleration sensor is detailed in the literature (Liu Y, Ji T, Xiaoing G, et al. calibration and compensation for accelerometer based on Kalman filter and a six-position method [ J ]. Piezoelectrics & Acoustoptics, 2016.).
Transfer function correction concept based on stabilized numerical integration
At present, a plurality of numerical integration methods are available, but some numerical integration methods are not suitable for practical complex signals in the engineering technical field. In order to improve the calculation accuracy, the integrated signal is segmented, and low-order polynomial interpolation is performed on each segment.
1. Traditional Simpson's method
The traditional simpson method fits the input signal by a parabolic segmentation method, which connects every 3 neighboring points with parabolas. As shown in fig. 3(a), for the time continuous function x (T), if the sampling interval is T, the simpson integral over the interval [0, KT ] can be expressed as:
in the formula (5), K is an even number.
Noting the integration result over the interval [ AT, NT-2T ], [ AT, NT-T ], [ AT, NT ] (A belongs to [0, K-2]) as y [ N-2], y [ N-1], y [ N ], the difference equation of the integration system can be expressed as:
equation (6) is a linear, invariant discrete-time system.
Z-transform equation (6) gives:
the transfer function of the conventional simpson method-based integration system can be expressed as:
as shown in fig. 3(b), the pole of the conventional simpson-based integration system is z ± 1, and on the unit circle, it is a critical stable system. The signal with the interference is integrated and the integration result is divergent. After the disturbance disappears, the output of the system has a constant deviation from the original equilibrium state or the output maintains constant amplitude oscillation. Therefore, the integration system is susceptible to numerical interference, and the integration result is unstable.
2. Correction of numerical integration method
The transfer function denominator of the traditional Simpson method has the factors z-1 and z +1, so the pole of the integral system is on the unit circle in the z plane, and is a critical stable system. Such an integration system is susceptible to numerical disturbances, and the integration result may be unstable.
The invention provides a stabilization numerical integration method, which respectively corrects the factors z-1 and z +1 in the denominator of a transfer function shown in a formula (8) into factors z-c and z + c, wherein c is a stabilization factor of a stabilization integration system, and c is more than 0 and less than 1.
After the modification, the transfer function shown in equation (8) can be expressed as:
as can be seen from equation (9), after the conventional simpson integration system is corrected by introducing the stability factor c, the pole z of the system falls within ± c of the unit circle, thereby forming a stable system. Under external interference, the system deviates from the original equilibrium state; when the external disturbance disappears, the system can automatically restore to the initial balance state. Therefore, the drift of the integration result can be suppressed by setting the stabilization factor and utilizing the automatic recovery capability of the stabilization system. Theoretically, the smaller c is, the better the stability of the integration system, but the larger c value will increase the integration error, and generally c is 0.995-0.996 (dawn by children, konnau, li xian, etc.. impulse wave pressure specific impulse finding method, discussion [ J ] missile and guidance bulletin, 2014,34(005): 94-97.).
Acceleration integral and integral error analysis based on stabilized numerical integral
1. Speed and displacement calculated by stabilized acceleration integral method
Z is inversely transformed for equation (9):
the velocity and displacement integrated with the acceleration sensor data using equation (10) can be expressed as:
the integral result of the expression (11) contains an error trend term, the speed and displacement results do not generate large offset, and the integral precision is improved.
2. Evaluation index of acceleration integral error
The acceleration integral error can be evaluated using the peak error, the difference error, and the absolute error.
The peak error err _ peak represents the average value of the relative difference between the peak value and the valley value of the true value of the integration result, that is:
in the formula (12), s (t) is the integration result; st(t) is true.
The difference error err _ diff represents the average of the integrated result peak and the true peak error, i.e.:
the absolute error err _ abs represents the ratio of the difference between the integration result and the true value to the true value, i.e.:
the evaluation index of the acceleration integral error is shown in the literature (Zhongjie. acceleration test integral displacement algorithm and application research thereof [ D ]. Chongqing university, 2013 ]).
A procedure for carrying out the method of the invention
Step 1: performing Kalman filtering and acceleration sensor parameter calibration on the acquired acceleration sensor original data;
step 2: correcting a traditional acceleration integral critical stabilization system by adopting a Simpson method based on stabilization numerical integration to construct a stabilization integration system;
and step 3: carrying out primary integration on the preprocessed acceleration sensor data by utilizing the constructed stabilization integration system to obtain speed, and carrying out secondary integration to obtain displacement;
and 4, step 4: and carrying out error analysis on the integration result by using the acceleration integration error evaluation index.
The beneficial effects of the present invention can be further illustrated by the following experiments:
let the acceleration signal a (t) be a simple harmonic signal, and the expression is:
a(t)＝5sin(10πt+0.5)+2cos(20πt+0.5)(15)
to verify the feasibility and accuracy of the present invention, the method described herein (stabilized Simpson method) was compared to the traditional Simpson method. The acceleration signals a (t) shown in the formula (15) were integrated once and twice by the above-described method, and the integration results were analyzed by the integration error evaluation indexes shown in the formulas (12) to (14), and the integration errors are listed in table 2.
TABLE 2 acceleration integral error comparison
It can be seen from table 2 that the velocity, the displacement peak error, the difference error and the absolute error of the stabilized numerical integration method proposed by the present invention are all smaller than those of the conventional simpson method. Therefore, the stabilization numerical integration method provided by the invention overcomes the influence of trend terms such as random noise, direct current component and the like on the integration result, and has feasibility.
Claims (5)
1. An acceleration sensor data processing method based on stabilized numerical integration is characterized by comprising the following steps:
(10) acceleration data acquisition: statically placing an acceleration sensor on a working platform, and collecting acceleration original data output by three shafts of the acceleration sensor within a period of time;
(20) preprocessing raw data: filtering the acquired acceleration original data by adopting a Kalman filtering algorithm to obtain filtered acceleration data;
(30) calibrating parameters of an acceleration sensor: establishing an error model of the acceleration sensor, and calibrating parameters of the acceleration sensor by adopting a six-position method;
(40) integration of acceleration data: performing primary integration on acceleration sensor data by adopting an acceleration sensor data processing method based on stabilization numerical integration to obtain speed; integrating the speed for the first time to obtain displacement;
(50) and (3) integral error analysis: and evaluating an acceleration integral error by adopting a peak error, a difference error and an absolute error.
2. The stabilized numerical integration-based acceleration sensor data processing method according to claim 1, characterized in that the (10) acceleration data acquisition step comprises:
(11) statically placing an acceleration sensor on a horizontal workbench, wherein the sampling frequency of the used acceleration sensor is 200 Hz;
(12) the acceleration sensor is connected with a computer through a data line;
(13) setting the data acquisition time to be 1 minute, and adopting data acquisition software to acquire data.
3. The acceleration sensor data processing method based on stabilized numerical integration according to claim 1, characterized in that the (30) acceleration sensor parameter calibration is mainly performed by a six-position method, comprising the specific steps of:
(31) constructing an error model of the acceleration sensor: an acceleration sensor error model is constructed according to the formula (1):
formula (1), (A)x，Ay，Az]TThe actual measured value is the actual measured value of the acceleration sensor; [ a ] Ax，ay，az]TIs the true value; [ a ] Ax0，ay0，az0]TZero bias in g; kx1，Ky1，Kz1，Kx2，Ky2，Kz2Is a mounting error coefficient; sx，Sy，SzIs a scale factor;
(32) the acceleration sensor is statically placed on a horizontal workbench by adopting a six-position method, and each position is placed for 1 minute;
(33) respectively collecting output data (A) of each axis of the acceleration sensor at each positionxi，Ayi，Azi)，i＝1，...，6；
(34) Calibrating parameters of an acceleration sensor: calibrating the parameters of the acceleration sensor according to the formula (2) to obtain the zero offset [ a ] of the acceleration sensorx0，ay0，az0]TMounting error Kx1，Ky1，Kz1，Kx2，Ky2，Kz2And scale factor Sx，Sy，Sz：
4. The stabilized numerical integration-based acceleration sensor data processing method according to claim 1, characterized in that the (40) acceleration data integration step comprises:
(41) transfer function modification: correcting a transfer function of an integral system of a Simpson numerical integration algorithm according to an equation (5) to construct a stable integral system:
equation (5), x (z) is the z-transform of the time continuous function x (t), y (z) is the z-transform of the time continuous function x (t) integrating the results over the sampling interval [0, KT ]; h (z) is the transfer function of the integral system; t is a sampling interval; c is a stability factor of the stable integral system;
(42) first integration: the acceleration sensor data is integrated once according to equation (6), and the resulting velocity is expressed as:
formula (6), a (n) is acceleration data; v (n) is velocity data; t is a sampling interval; c is a correction factor of the stable integral system;
(43) second integration: the displacement can be obtained by integrating the velocity again according to the formula (7); the displacements obtained by reintegrating the velocity shown in equation (6) by the stabilization integration system constructed by the stabilization simpson method shown in equation (5) can be expressed as:
formula (7), v (n) is velocity; s (n) is a displacement; t is a sampling interval; c is a stability factor for stabilizing the integration system.
5. The stabilized numerical integration-based acceleration sensor data processing method according to claim 1, characterized in that the (50) integration error analysis step comprises:
(51) evaluating the error of the acceleration integration result according to the peak error, the difference error and the absolute error shown in the formulas (8) to (10):
the difference error err _ diff represents the average of the integrated result peak and the true peak error, i.e.:
the absolute error err _ abs represents the ratio of the difference between the integration result and the true value to the true value, i.e.:
the expressions (8) to (10), s (t) being the integration result; st(t) is true;
(52) and comparing the integration result with the peak error, the difference error and the absolute error of the integration result of the traditional Simpson method.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115597571A (en) * | 2022-12-15 | 2023-01-13 | 西南应用磁学研究所（中国电子科技集团公司第九研究所）（Cn） | Method for quickly calibrating and compensating error and installation error of electronic compass sensor |
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