CN114781432A - Displacement resolving method based on multi-source information fusion and trend-removing fluctuation analysis - Google Patents
Displacement resolving method based on multi-source information fusion and trend-removing fluctuation analysis Download PDFInfo
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Abstract
The invention provides a displacement resolving method based on multi-source information fusion and trend-removing fluctuation analysis, which can be applied to the fields of industrial automation, building bridges, earthquake monitoring, rehabilitation and nursing and the like. The method includes the steps that acceleration and angle data collected by a three-axis attitude sensor are utilized, space pose transformation is utilized to realize data fusion, the influence of gravity acceleration components in the acceleration data is eliminated, linear interpolation functions, a trend-removing fluctuation analysis method and a Kalman filtering algorithm are utilized to obtain acceleration data with equal time intervals, trend terms and noise in the acceleration data are eliminated, and finally a stable numerical integration method is utilized to calculate displacement. According to the method, on the premise that an external displacement sensor is not adopted, the actual displacement is obtained by resolving through fusing self acceleration and angle attitude information, the accurate solution of the spatial displacement is realized, and the defects that the displacement sensor can only measure one-dimensional displacement and the installation position space is limited are overcome.
Description
Technical Field
The invention relates to the technical field of sensors and signal processing, in particular to a displacement resolving method based on multi-source information fusion and detrending fluctuation analysis.
Background
With the continuous development of sensor technology, various sensors are continuously applied to various fields, wherein the application range of displacement sensors is quite wide, and the displacement sensors are commonly used in the aspects of industrial automation, building bridges and the like. The displacement sensor outputs electric signals with different magnitudes according to the magnitude of the displacement, then solves the magnitude of the displacement, and is mainly used for measuring physical quantities such as length, distance, vibration, speed, direction and the like of equipment such as an injection molding machine, a hydraulic machine, hardware machinery, rolling rod adjustment of a steel mill, a shield machine and the like. However, the displacement sensor is generally limited by various environmental conditions when the displacement sensor is applied to obtain a displacement signal, because the displacement sensor has the defects of large volume, inconvenience in installation and use in small equipment, easily limited measuring distance, incapability of measuring two-dimensional and three-dimensional motion states and the like. Besides directly obtaining the displacement signal through the displacement sensor, the displacement sensor can also obtain an acceleration signal through an acceleration sensor with a wider application field, and the obtained acceleration signal is used for integration to obtain the displacement signal. In the existing method for obtaining displacement by integrating acceleration, an acceleration sensor is mostly fixed on a test platform, and the obtained acceleration data is used for analysis and processing, so that the method is poor in flexibility and difficult to transplant to a movable working condition environment for working. For the acceleration sensor with the inclined vertical axis, most of the existing methods use a high-pass filter to carry out baseline adjustment, so that not only is baseline error removed, but also low-frequency content including residual displacement in a signal is eliminated, and the integral result is smaller than a true value. Therefore, aiming at the characteristics of the acceleration sensor and the numerical integration, the invention provides a stable numerical integration method based on multi-source information fusion and trend-removing fluctuation analysis, which can be separated from a test bed to realize the movement and portability of the sensor, is used for realizing the displacement solution of the one-dimensional, two-dimensional and three-dimensional movement of the acceleration sensor, and is the key for further solving the equipment displacement information under the condition of limited position space.
Disclosure of Invention
The invention provides a displacement solving method combining information fusion and trend-removing fluctuation analysis, aiming at solving the problem of realizing one-dimensional, two-dimensional and three-dimensional displacement solving according to time information, acceleration information and angle information output by an acceleration sensor under the condition of only adopting the acceleration sensor, and providing a new thought and method for the displacement solving of equipment which is limited by a position space and is not suitable for adopting the displacement sensor.
The invention provides a displacement resolving method based on multi-source information fusion and detrended fluctuation analysis, which specifically comprises the following steps:
the method comprises the steps of firstly, detecting obtained attitude data, carrying out data preprocessing, and deleting a plurality of repeated data at the same moment.
And step two, carrying out data fusion according to the obtained acceleration and the space attitude information, and eliminating the gravity acceleration component in the obtained acceleration.
And thirdly, carrying out interpolation processing according to the time data and the acceleration data to obtain acceleration data with equal time intervals.
And step four, eliminating trend components in the acceleration according to a trend-removing fluctuation analysis technology.
And fifthly, eliminating the noise in the acceleration according to a Kalman filtering method.
And sixthly, integrating the acceleration data according to a stable numerical integration method to solve the displacement.
The invention has the beneficial effects that:
(1) the acceleration sensor with the smaller volume is adopted, compared with a displacement sensor, the acceleration sensor is less influenced by the position space and is convenient to transplant, and the wireless communication with an upper computer can be realized by combining a micro wireless transmission module.
(2) The acceleration and the corresponding angle information fusion algorithm are combined, the influence of the gravity acceleration is eliminated from the aspect of pose transformation, and the influence of the gravity acceleration component change caused by the acceleration sensor space attitude transformation in the motion process is eliminated.
(3) By adopting the trend-removing fluctuation analysis and Kalman filtering method, the drift and noise of the acceleration sensor in the long-time working process are eliminated, so that the result of solving the displacement in the long-time working process is more accurate.
(4) The transfer function considers the cause of drift in the integration process of the traditional numerical integration method, and the improved integration algorithm becomes a stable system by correcting the integration parameters.
Drawings
FIG. 1 is a displacement calculation flow diagram of the present invention;
FIG. 2 is a schematic diagram of the present invention showing the transformation of the Cartesian coordinate system of the acceleration sensor;
FIG. 3 is acceleration data and angle data collected when the acceleration sensor is used in the present invention to move along the X-axis;
FIG. 4 is acceleration data and angle data collected when the acceleration sensor is used in the present invention to move along the Y-axis;
FIG. 5 is acceleration data and angle data collected when the acceleration sensor is used to move along the X-axis and the Y-axis at an included angle of-61 degrees in the present invention;
FIG. 6 is the acceleration data and angle data collected when the acceleration sensor is used in the present invention to move along the X-axis and Y-axis with an included angle of 53 degrees;
FIG. 7 is acceleration data collected when the acceleration sensor is used to move along the X-axis in the present invention and acceleration data processed by the method of the present invention;
FIG. 8 is acceleration data collected when the acceleration sensor is used in the present invention to move along the Y-axis and acceleration data processed by the method of the present invention;
FIG. 9 is the acceleration data collected when the acceleration sensor is used to move along the X-axis and the Y-axis at an included angle of-61 degrees and the acceleration data processed by the method of the present invention;
FIG. 10 is a graph of acceleration data collected during a 53 degree motion along the X-axis and Y-axis using an acceleration sensor in accordance with an embodiment of the present invention and acceleration data processed by the method of the present invention;
FIG. 11 is a comparison graph of the integral displacement and the actual displacement obtained after calculation by the method of the present invention when the acceleration sensor moves along the X-axis;
FIG. 12 is a comparison graph of the integral displacement and the actual displacement obtained after calculation by the method of the present invention when the acceleration sensor moves along the Y-axis in the present invention;
FIG. 13 is a comparison graph of the integral displacement and the actual displacement obtained after calculation by the method of the present invention when the acceleration sensor moves along the X axis and the Y axis with an included angle of-61 degrees;
FIG. 14 is a comparison graph of the integral displacement and the actual displacement obtained after calculation by the method of the present invention when the acceleration sensor moves along the X axis and the Y axis with an included angle of 53 degrees;
FIG. 15 is a three-dimensional graph of a displacement trajectory obtained by resolving acceleration data acquired when an acceleration sensor is adopted to move along four different directions according to the present invention.
Detailed Description
The following describes the displacement solution method based on information fusion and detrending fluctuation analysis in detail with reference to the accompanying drawings and embodiments.
Step one, detecting time data in the obtained data samples, deleting repeated data groups in the data transmission and receiving process, only keeping a group of effective data at the same moment, processing the time data into absolute time, taking the first group of data as initial data, and setting a time node to be 0.
And step two, introducing a concept of a rotation matrix in robot kinematics to eliminate a gravity acceleration component contained in the original acceleration data. As shown in FIG. 2, the acceleration sensor is designed with a Cartesian coordinate system, and the X-ray winding can be determined according to the right-hand rule0,Y0,Z0In the positive direction of the axis rotation, the rotation angles are denoted α, β, γ, respectively.
Around X0,Y0,Z0The axes are respectively rotated by alpha, beta and gamma, and the obtained rotation matrixes are respectively:
from an initial coordinate system 0-X0Y0Z0First winding X0Rotation of axis alpha, rewind Y0Rotation of axis beta, finally about Z0And rotating the axis gamma to obtain a real pose coordinate system 0-XYZ in the actual operation process. The relationship between the finally obtained rotation matrix R and the two coordinate systems is respectively as follows:
Accinit＝R·Accgra (5)
wherein AccinitIs the gravitational acceleration component of the gravitational acceleration in each axis in the world coordinate system, AccgraThe gravity acceleration component of the gravity acceleration in each axis in the actual pose coordinate system is shown. Due to the influence of gravity, when the acceleration sensor is static in a world coordinate system, the acceleration sensor always has a value of g, a direction and Z0Acceleration with coincident positive axes, i.e. Accinit＝[00g]T. The gravitational acceleration component of the gravitational acceleration in each axis in the actual pose coordinate system can be expressed as:
and after the gravity acceleration component of each axis in the actual pose coordinate system is removed, the acceleration of each axis is:
Accact＝Acc-Accgra＝[Accx+gsinβAccy-gcosβsinαAccz-gcosαcosβ]T (7)
wherein Acc is [ Acc ═ Accx Accy Accz]T，Accx,Accy,AcczRespectively representing the acquired triaxial acceleration data.
And step three, the time intervals of the acceleration data after the gravity acceleration component is eliminated are possibly unequal, and known acceleration data and time data are subjected to interpolation processing, so that the acceleration data in the subsequent integration process have the same time interval, and the simplicity of the integration process and the accuracy of the integration result can be ensured to a certain extent. Using time data and acceleration data to do piecewise linear interpolation, the interpolation function phi (x) is in each small region xk,xk+1]The above can be expressed as:
wherein x isk(k-0, 1.., n) represents a time node, fk(k ═ 0,1,. ang., n) denotes in xkAcceleration at the moment of time. The entire time interval t is represented by an interpolated basis function l (x)s,te]The interpolation function above is:
wherein li(x) The interpolation basis function for the ith time node (i ═ 0, 1.. times, n) can be expressed as:
wherein t iss,teRespectively representing the start time and the end time of the whole time interval. The equal interval time and the corresponding acceleration data can be determined by a linear interpolation function according to requirements.
Step four, the data output by the acceleration sensor in the long-time operation process contains certain trend components, if the trend components are not filtered in the analysis process, the actual data gradually deviates from the true value along with the increase of time, and larger deviation can be caused in the subsequent integration process. Therefore, a trend component in the acceleration data is removed by applying a trend-removing fluctuation analysis technology to the interpolated acceleration data. The process of the detrending fluctuation analysis method is as follows:
for a sequence of length N phijJ ═ 1,2,.., N }, a new sequence is created:
wherein,
is the original sequence phijOf the average value of (a).
Dividing the new sequence y (m) into non-overlapping equal-length subintervals with the length s, and dividing the sequence with the length N into NsInt (N/s) subintervals. Because the sequence length N is not necessarily divided by the sub-interval length s, in order to ensure that the original sequence information is not lost, the sequence can be divided from the end of the sequence back to the front again to obtain 2NsAnd (4) sub-intervals.
For each subinterval v (v ═ 1, 2., 2N)s) The obtained local trend function can be a polynomial of first order, second order or higher order. Eliminating the trend in each subinterval, and calculating the variance mean value F2(v, s) are:
determining a complete sequence of a fluctuation function of order q:
wherein q can take any non-zero real number. When q is 0, formula (14) becomes:
in the actual calculation, for each subinterval v (v ═ 1, 2., 2N)s) Q may be taken to be any non-zero real number when the data of (a) are subjected to polynomial regression fitting.
And step five, the original acceleration signal contains noise generated in the data acquisition process, and the noise signal is processed by adopting a Kalman filtering algorithm. The algorithm has the advantages of small calculation amount and good real-time performance. The estimated value of the future motion state can be continuously corrected by utilizing the actual motion parameters, and the estimation precision is improved on the premise of considering both real-time property and stability.
The state vector prediction equation can be expressed as:
the state vector covariance matrix prediction can be expressed as:
the kalman gain matrix may be expressed as:
the state vector update equation can be expressed as:
the state vector covariance update equation can be expressed as:
wherein,
which is indicative of the state of the prediction,
representing the state estimate, a representing the state transition matrix,
representing the prediction error covariance, PkDenotes the estimation error covariance, Q denotes the process error, KkDenotes the Kalman gain, H denotes the measurement matrix, R denotes the measurement error, akDenotes the measured value, I denotes the identity matrix.
Step six, integrating the processed acceleration data by adopting a trapezoidal method, wherein for a time continuous function x (T) with a sampling interval of T, a trapezoidal integral formula in the interval [0, KT ] is as follows:
y represents the value obtained after integration of the continuous function x (T) for time with a sampling interval T. The transfer function of the trapezoidal integral equation is:
as can be seen from the transfer function described in equation (22), the pole of the transfer function is located on the unit circle, i.e. in the critical steady state, which is prone to cause divergence during integration. The velocity v (j) and the displacement s (j) integrated for the j (j) th acceleration a (j) are expressed by the following formula:
v(j)＝T[a(j)+a(j-1)]/2+ωv(j-1) (23)
s(j)＝T[v(j)+v(j-1)]/2+ωs(j-1) (24)
wherein ω is a stability factor.
Examples
The method of the invention is adopted to carry out stable numerical integration calculation on the data acquired by the triaxial acceleration sensor as follows:
the testing instrument with the built-in three-axis acceleration sensor is adopted to do four groups of cyclic reciprocating motions, the motions are respectively carried out along the directions with included angles of-61 degrees and 53 degrees between the X axis and the Y axis and between the X axis and the Y axis, and the time data, the acceleration data and the angle data are sent by the testing instrument through the wireless module. The time data is checked, and the repeated data is subjected to deletion processing, so that the acceleration data and the angle data are obtained as shown in fig. 3-6. In order to verify the correctness of the method, the actual displacement data acquired by the laser displacement sensor is used as reference.
And (4) obtaining triaxial acceleration data without the gravity acceleration component according to the formula (7) aiming at the obtained triaxial acceleration data and triaxial angle data corresponding to the triaxial acceleration data. Since the time data intervals obtained by the acceleration sensors are unequal, triaxial acceleration interpolation data with the time interval T of 0.01s is obtained by linear interpolation. And then removing trend components in the interpolation data by using a trend removing fluctuation analysis technology, wherein q is 15. And finally processing the acceleration data by adopting a Kalman filtering algorithm with a process error Q of 0.001 and a measurement error R of 0.01. As in fig. 7-10.
And (3) solving the displacement by using a stable numerical integration algorithm of an equation (23) and an equation (24) according to the obtained final acceleration signal, wherein a stability factor omega is 0.996, comparing the stable numerical integration algorithm with displacement data obtained by the laser displacement sensor, and showing the integration result and an actual displacement result in fig. 11-14 and showing a three-dimensional result in fig. 15.
The peak error, the difference error, the absolute error and the mean square error are quoted to evaluate the acceleration integral result error by adopting the method of the invention.
The peak error err _ peak represents the average of the relative differences of the peak of the integration result and the peak of the truth value:
the difference error err _ diff represents the average of the integrated result value and the true value difference:
the absolute error err _ abs represents the ratio of the difference between the integrated result and the true value to the true value:
the difference in mean square error MSE represents the degree to which the integration result differs from the true value:
wherein s (t) represents the integration result, stAnd (t) represents a true value, and the displacement data acquired by the laser displacement sensor is a true value by default.
The error results are calculated from equation (25) to equation (28) in table 1.
TABLE 1 error results
As can be seen from Table 1, the method provided by the invention has the advantages that the accuracy of the integration result is obviously improved, and the average values of err _ peak, err _ diff, err _ abs and MSE are respectively improved by 91.68%, 63.41%, 72.40% and 86.83%.
Claims (10)
1. A displacement resolving method based on multi-source information fusion and trend-removing fluctuation analysis is characterized by comprising the following steps:
firstly, detecting the obtained attitude data, carrying out data preprocessing, and deleting a plurality of repeated data at the same moment;
step two, carrying out data fusion according to the obtained acceleration and the space attitude information, and eliminating a gravity acceleration component in the obtained acceleration;
performing interpolation processing according to the time data and the acceleration data to obtain acceleration data with equal time intervals;
eliminating trend components in the acceleration according to a trend-removing fluctuation analysis technology;
fifthly, eliminating noise in acceleration according to a Kalman filtering method;
and sixthly, performing integral processing on the acceleration data according to a stable numerical integration method to solve the displacement.
2. The displacement calculation method based on multi-source information fusion and detrending fluctuation analysis according to claim 1, wherein: in the first step, the method specifically comprises the following steps: detecting time data in the obtained data samples, deleting repeated data groups in the data transmission and receiving processes, only retaining a group of valid data at the same time, and processing the time data into absolute time.
3. The displacement calculation method based on multi-source information fusion and detrending fluctuation analysis according to claim 1, wherein: in the second step, the method specifically comprises the following steps: introducing a concept of a rotation matrix in robot kinematics to eliminate a gravity acceleration component contained in original acceleration data; the acceleration sensor is designed by adopting a Cartesian coordinate system, and the X winding is determined according to the right-hand rule0,Y0,Z0The positive direction of the axis rotation, the rotation angles are denoted as α, β, γ, respectively;
around X0,Y0,Z0The axes are rotated by α, β, γ, respectively, and the resulting rotation matrices are:
from an initial coordinate system 0-X0Y0Z0First winding X0Rotation of the shaft by a, and then by Y0Rotation of axis beta, finally around Z0Rotating the axis gamma to obtain a real pose coordinate system 0-XYZ in the actual operation process; the relationship between the finally obtained rotation matrix R and the two coordinate systems is respectively as follows:
Accinit＝R·Accgra (5)
wherein AccinitIs the gravitational acceleration component of the gravitational acceleration in each axis in the world coordinate system, AccgraThe gravity acceleration component of the gravity acceleration in each axis in the actual pose coordinate system is shown.
4. The displacement solution method based on multi-source information fusion and detrended fluctuation analysis of claim 3, wherein: in the second step, the method further comprises the following steps: because of the influence of gravity, when the acceleration sensor is static in a world coordinate system, the acceleration sensor always has a size g, a direction and a Z0Acceleration with coincident positive directions of axes, i.e. Accinit＝[00g]T(ii) a Then the gravitational acceleration component of the gravitational acceleration in each axis in the actual pose coordinate system is expressed as:
and after the gravity acceleration component of each axis in the actual pose coordinate system is removed, the acceleration of each axis is:
Accact＝Acc-Accgra＝[Accx+g sinβ Accy-g cosβsinα Accz-g cosαcosβ]T (7)
wherein Acc ═ Accx Accy Accz]T，Accx,Accy,AcczRespectively representing the acquired triaxial acceleration data.
5. The displacement calculation method based on multi-source information fusion and detrending fluctuation analysis according to claim 1, wherein: in the third step, the concrete steps are as follows: the time intervals of the acceleration data after the gravity acceleration component is eliminated are possibly unequal, known acceleration data and time data are subjected to interpolation processing, the same time interval among the acceleration data in the subsequent integration process is ensured, and the simplicity and the accuracy of the integration process and the accuracy of the integration result are ensured to a certain extent; using time data and acceleration data to do piecewise linear interpolation, the interpolation function phi (x) is in each small region [ xk,xk+1]The above is represented as:
wherein x isk(k-0, 1.., n) represents a time node, fk(k ═ 0, 1.., n) denotes in xkAcceleration at a moment; the entire time interval t is represented by an interpolated basis function l (x)s,te]The interpolation function above is:
wherein li(x) An interpolation basis function for the ith time node (i ═ 0, 1.., n), expressed as:
wherein t iss,teRespectively representing the starting time and the ending time of the whole time interval; and determining the equal interval time and the corresponding acceleration data according to the requirement by a linear interpolation function.
6. The displacement calculation method based on multi-source information fusion and detrending fluctuation analysis according to claim 1, wherein: in the fourth step, the concrete steps are as follows: the data output by the acceleration sensor in the long-time running process contains certain trend components, and the trend components in the acceleration data need to be removed by applying a trend-removing fluctuation analysis technology to the interpolated acceleration data; the process of the detrending fluctuation analysis method is as follows:
for a sequence of length N φjJ ═ 1,2,.., N }, a new sequence is created:
wherein,
is the original sequence phijThe mean value of (a);
dividing the new sequence y (m) into non-overlapping equal-length subintervals with the length s, and dividing the sequence with the length N into NsInt (N/s) subintervals; because the sequence length N is not necessarily divided by the sub-interval length s, in order to ensure that the original sequence information is not lost, the sequence is divided from the tail end to the front again to obtain 2NsAnd (4) sub-intervals.
7. The displacement solution method based on multi-source information fusion and detrended fluctuation analysis of claim 6, wherein: in step four, the method further comprises: for each subinterval v (v ═ 1, 2., 2N)s) The obtained local trend function is a plurality of first order, second order or higher orderA formula; eliminating the trend in each subinterval, and calculating the variance mean value F2(v, s) are:
determining a full sequence of fluctuation functions of order q:
wherein q is any non-zero real number.
8. The displacement calculation method based on multi-source information fusion and detrending fluctuation analysis of claim 7, wherein: in the fourth step, the method further comprises: when q is 0, equation (14) becomes:
in the actual calculation, for each subinterval v (v ═ 1, 2., 2N)s) When polynomial regression fitting is carried out on the data, any non-zero real number is taken as q.
9. The displacement solution method based on multi-source information fusion and detrended fluctuation analysis of claim 1, wherein: in the fifth step, the method specifically comprises the following steps: the original acceleration signal comprises noise generated in the data acquisition process, and the noise signal is processed by adopting a Kalman filtering algorithm; the algorithm has the advantages of small calculated amount and good real-time performance; the estimation value of the future motion state is continuously corrected by utilizing the actual motion parameters, and the estimation precision is improved on the premise of considering real-time performance and stability;
the state vector prediction equation is expressed as:
the state vector covariance matrix prediction is expressed as:
the kalman gain matrix is expressed as:
the state vector update equation is expressed as:
the state vector covariance update equation is expressed as:
wherein,
which is indicative of the state of the prediction,
representing the state estimate, a representing the state transition matrix,
representing the prediction error covariance, PkRepresenting estimation error covariance, Q representing process error, KkDenotes the Kalman gain, H denotes the measurement matrix, R denotes the measurement error, akDenotes the measured value, I denotes the identity matrix.
10. The displacement calculation method based on multi-source information fusion and detrending fluctuation analysis according to claim 1, wherein: in the sixth step, specifically: integrating the processed acceleration data by adopting a trapezoidal method, wherein for a time continuous function x (T) with a sampling interval of T, a trapezoidal integral formula in the interval [0, KT ] is as follows:
wherein y represents a value obtained by integrating a time continuous function x (T) with a sampling interval of T; the transfer function of the trapezoidal integral formula is:
the transfer function is obtained by the formula (22), and the pole of the transfer function is positioned on the unit circle, namely in a critical stable state, so that divergence is easily caused in the integration process; the velocity v (j) and the displacement s (j) integrated for the j (j) th acceleration a (j) are expressed by the following formula:
v(j)＝T[a(j)+a(j-1)]/2+ωv(j-1) (23)
s(j)＝T[v(j)+v(j-1)]/2+ωs(j-1) (24)
where ω is a stability factor.
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| CN106500695A (en) * | 2017-01-05 | 2017-03-15 | 大连理工大学 | A kind of human posture recognition method based on adaptive extended kalman filtering |
| CN109550219A (en) * | 2018-11-30 | 2019-04-02 | 歌尔科技有限公司 | A kind of determination method, system and the mobile device of motion information |
| CN110887652A (en) * | 2019-12-04 | 2020-03-17 | 武汉大学 | Interactive multi-model detection method for vibration detection and displacement extraction of accelerometer |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106500695A (en) * | 2017-01-05 | 2017-03-15 | 大连理工大学 | A kind of human posture recognition method based on adaptive extended kalman filtering |
| CN109550219A (en) * | 2018-11-30 | 2019-04-02 | 歌尔科技有限公司 | A kind of determination method, system and the mobile device of motion information |
| CN110887652A (en) * | 2019-12-04 | 2020-03-17 | 武汉大学 | Interactive multi-model detection method for vibration detection and displacement extraction of accelerometer |
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