A multi-dimensional force sensor hybrid excitation dynamic calibration method for reducing noise influence

Abstract

The application discloses a multi-dimensional force sensor mixed excitation dynamic calibration method for reducing noise influence, constructs a mixed excitation load table with row orthogonality and row full rank, adopts mixed excitation to perform dynamic calibration experiment on the multi-dimensional force sensor, and calculates the frequency response function of the sensor according to the dynamic calibration experiment data. Firstly, a plurality of excitation load direction vectors are designed for the multi-dimensional force sensor, so as to ensure that the matrix formed by the plurality of excitation load direction vectors is row orthogonal and row full rank. Secondly, each element load is valued based on the excitation load direction vectors, and a mixed excitation load table is constructed. Thirdly, loading points are designed on a measuring end tool of the sensor according to the mixed excitation load table, and mixed excitation dynamic calibration experiment is performed to obtain data. Finally, the frequency response function of each element of the sensor is calculated by using a frequency domain least square method according to all dynamic calibration experiment data of the sensor, and the dynamic characteristics of the sensor are obtained. The method provides a simple dynamic calibration method for the multi-dimensional force sensor, and the noise influence is reduced.

Description

Technical Field

[0001] This invention relates to dynamic calibration technology for sensors, and in particular to a hybrid excitation dynamic calibration method for multidimensional force sensors that can reduce the impact of noise. By using hybrid excitation, the difficulty of dynamic calibration experiments for multidimensional force sensors is reduced. The frequency response curves of each channel are obtained by calculating the frequency response function of the sensor, thereby providing a simple hybrid excitation dynamic calibration method for multidimensional force sensors that can reduce the impact of noise. Background Technology

[0002] A multidimensional force sensor is a type of force sensor that can decompose a spatial vector force into multiple force and torque components along a Cartesian coordinate system and measure them simultaneously. It is widely used in production, testing, and experimentation. To evaluate the actual dynamic performance of a multidimensional force sensor, dynamic calibration experiments are required to obtain its dynamic input and output data. Based on this, a dynamic mathematical model can be established or its frequency response function can be calculated to obtain its dynamic characteristics. For multidimensional force sensors, a unit-excitation dynamic calibration method is typically used to perform dynamic calibration experiments sequentially in each direction. However, to ensure that the dynamic performance of the sensor obtained through dynamic calibration closely approximates its actual operating performance, the tooling conditions of the force sensor in the dynamic calibration experiment must be as close as possible to or identical to the tooling conditions in its actual operation. Therefore, unit-excitation dynamic calibration is often quite difficult when dealing with sensor tooling of various shapes. A Chinese invention patent discloses a hybrid excitation dynamic calibration method for a strain gauge six-dimensional force sensor (Yang Shuanglong, Wang Junxiang, et al. A hybrid excitation dynamic calibration method for a strain gauge six-dimensional force sensor, application number: CN202110277339.6, application date: 2021.5.28). The method includes hybrid excitation direction table design → hybrid excitation dynamic calibration experiment → dynamic hybrid excitation load identification → frequency response function calculation. This hybrid excitation dynamic calibration method can reduce the experimental requirements for dynamic calibration of six-dimensional force sensors and meet the calibration needs of six-dimensional force sensors with different tooling structures. However, the above-mentioned hybrid excitation dynamic calibration method only considers reducing the difficulty and requirements of the dynamic calibration experiment of the six-dimensional force sensor, but does not consider the impact of noise on the experiment in hybrid excitation dynamic calibration. This results in the frequency response estimation noise of each channel not only coming from the experimental data in its own direction, but also possibly from the superposition of noise from data in other directions, thus amplifying the noise effect. Summary of the Invention

[0003] This invention aims to address the problem that existing multidimensional force sensor hybrid excitation dynamic calibration methods may cause noise superposition in frequency response estimation, and provides a multidimensional force sensor hybrid excitation dynamic calibration method that can reduce the impact of noise.

[0004] The key improvement of this invention lies in the hybrid excitation load design, which reduces the noise impact in the dynamic calibration of multi-dimensional force sensors using hybrid excitation. The technical solution adopted in this invention is as follows: First, for the sensor and its tooling structure, excitation load direction vectors are designed according to the principle of ease of implementation. These vectors indicate the direction of the excitation load applied to the force sensor in a single dynamic calibration experiment, including hybrid excitation load direction vectors of "single force-single torque" or "single force-double torque" loading, and can also include easily implemented unit excitation load direction vectors. The "single force-single torque" hybrid excitation load direction vectors adopt a paired design principle, while the "single force-double torque" hybrid excitation load direction vectors adopt a grouping principle of four, ensuring that the row vectors of their combined matrix are orthogonal. The total number of excitation load direction vectors is greater than or equal to the dimension of the force sensor, and the non-zero load directions should cover all measurement directions of the force sensor, ensuring that the matrix they form has full row rank. Secondly, load values ​​are assigned according to the excitation load direction vector to obtain the corresponding excitation load vector. The scale of the excitation load vector is expanded by assigning multiple different load values ​​to each excitation load direction vector. All excitation load vectors are combined as column vectors to form a hybrid excitation load matrix, thereby constructing a hybrid excitation load table for dynamic calibration of the multidimensional force sensor. Then, according to the loading requirements of each excitation load vector in the hybrid excitation load table, loading points are designed on the measuring end fixture of the sensor. The corresponding dynamic loads are applied to the sensor in sequence according to the hybrid excitation load table to conduct dynamic calibration experiments and obtain dynamic calibration experiment data. Finally, based on all the dynamic calibration experiment data of the sensor, the frequency response function of each measurement channel of the sensor is calculated using the frequency domain least squares method to obtain the dynamic characteristics of the sensor.

[0005] The technical process of this invention is as follows: 1. Excitation load direction vector design → 2. Construction of hybrid excitation load table → 3. Hybrid excitation dynamic calibration experiment → 4. Frequency response function calculation. Figure 1 As shown.

[0006] The excitation load direction vector design 1 refers to designing multiple direction excitation loads corresponding to different directions based on the requirements for dynamic calibration of the multi-dimensional force sensor in various directions. Where n is the dimension of the multidimensional force sensor, i.e., the number of excitation elements; the excitation elements include the force elements and torque elements measured by the force sensor; i = 1, 2, 3, ..., m, where m is the number of different excitation load direction vectors; ε i1 ε i2 ..., ε in In order to represent The corresponding excitation directions on the 1st, 2nd, ..., nth elements of the multidimensional force sensor have values ​​of 1, 0, and -1, respectively, representing positive excitation, no excitation, and negative excitation. The design follows the principle that dynamic loading of multi-dimensional force sensors is easy to implement under tooling conditions. It mainly includes mixed excitation load direction vectors of "single force-single torque" or "single force-double torque" loading, and can also include easily implemented unit excitation load direction vectors. All such excitation loads can be achieved by applying a force along a specified direction at a specified loading point on the multi-dimensional force sensor, which is easy to control.

[0007] "Single force - single moment" hybrid excitation load direction vector In this case, only one force element and its resulting torque element have an excitation direction of 1 or -1, while all other excitation elements have a direction of 0; the "single force-single torque" hybrid excitation load direction vector The design follows a one-to-two approach, meaning it designs two non-zero excitation elements with identical "single force-single moment" hybrid excitation load direction vectors. There is exactly one excitation element between the two with opposite excitation directions, thus making and The resulting matrix has orthogonal row vectors.

[0008] "Single force - dual moment" hybrid excitation load direction vector In this case, only one force element and the two torque elements it generates have an excitation direction of 1 or -1, while all other excitation elements have a direction of 0; the direction vector of the "single force-double torque" hybrid excitation load is... Based on a set of four designs, that is, designing four non-zero excitation elements with the same "single force-double moment" hybrid excitation load direction vector. and ensure The combined matrix row vectors are orthogonal; among the four mixed excitation load direction vectors, the excitation directions of the excitation elements that are not zero are preferably two positive and two negative.

[0009] Element excitation load direction vector Only one force element or torque element has an excitation direction of 1 or -1, while the other excitation elements are all 0.

[0010] All excitation load direction vectors A matrix that is a combination of column vectors should have full row rank.

[0011] The hybrid excitation load table construction 2 is based on the design of each excitation load direction vector. Perform load assignment to obtain the corresponding excitation load vector F i The combined excitation load table F is obtained; let L i =[l i1 ,l i2 ,...,l in ] T In response to Given the excitation load amplitude vectors of each excitation element, and the symbol "⊙" denotes vector dot product, then:

[0012] "Single force - single moment" hybrid excitation load vector pair

[0013] In the "single force-dual torque" hybrid excitation load vector group

[0014] Element excitation load vector

[0015] For each excitation load direction vector If each is configured with q different excitation load amplitude vectors L i Then we obtain M = q·m excitation load vectors F. i ; to convert all excitation load vectors F i The hybrid excitation load table F = [F1, F1, ..., F1] is obtained by combining column vectors. M ], which is an n×M dimensional matrix; under the design of the excitation load direction vector design 1, F is a row orthogonal, row full-rank matrix, thus providing the prerequisite for noise decoupling and suppression when estimating the frequency response function based on the sensor hybrid excitation dynamic calibration experimental data.

[0016] The hybrid excitation dynamic calibration experiment 3 refers to the process of constructing each excitation load vector F in the hybrid excitation load table F based on the hybrid excitation load table construction 2. i To meet the loading requirements, a corresponding loading point P is designed on the tooling of the force sensor. i and at loading point P i The corresponding dynamic excitation load F is applied to the sensor. i Collect relevant dynamic calibration experimental data, specifically including: tooling loading point design 5, sensor dynamic excitation 6, sensor dynamic response acquisition 7.

[0017] Tooling loading point design 5: This refers to selecting or designing the tooling on the sensor's measuring end, which is related to the direction vector of the excitation load. Corresponding loading surface S i On loading surface S i Design and excitation load vector F i The corresponding loading point P i The principles are as follows:

[0018] ① Loading surface S i All perpendicular to the sensor coordinate system Oxyz and The coordinate axes are parallel to the directions of force elements whose excitation direction is not zero.

[0019] ②On the loading surface S iAccording to F i The magnitudes of the force element and moment element determine the loading point P. i Location;

[0020] ③As long as principles ① and ② above are satisfied, the loading surface S corresponding to the mixed excitation load Fi of group M is... i They are partially the same.

[0021] Sensor dynamic excitation 6: This refers to sequentially loading the sensor measuring end tooling surface S according to the hybrid excitation load table F. i Loading point P on i Apply dynamic excitation force u i This generates a corresponding dynamic excitation load F. i This was done to conduct dynamic calibration experiments on the sensor. The dynamic force was applied using either an impact method or a step method, specifically by applying force to the sensor's tooling loading surface S. i Upper P i A perpendicular line to the loading surface S is applied at the position. i The impact force or step force.

[0022] Sensor dynamic response acquisition 7: This refers to simultaneously acquiring the sensor's dynamic excitation input u while applying dynamic excitation to the sensor. i and the dynamic response output y of each measurement element i The sensor's dynamic excitation input u i That is, the applied dynamic force signal, and the dynamic response output y i The voltage signals output by each measuring element of the sensor; the number of points in the continuously acquired dynamic input and output signal sequences of the sensor is the same, N, and N must ensure that the signal has sufficient length before and after the impact or step moment and that the signals output by each element of the sensor have entered a steady state; u i Let y be a 1×N vector. i It is an n×N matrix. Based on the dynamic excitation force u... i and loading point P i The dynamic excitation load F is obtained by calculating the position coordinates. i The corresponding multidimensional excitation load sequence U i , is an n×N dimensional matrix; the dynamic response y is evaluated using the sensor's static correction coefficients. i The multidimensional dynamic response load sequence Y under dynamic excitation is obtained by making corrections. i , is an n×N dimensional matrix; i = 1, 2, ..., M.

[0023] The frequency response function calculation 4 involves calculating the frequency points f based on the input-output relationship Y(f)=G(f)U(f) of the multi-dimensional force sensor using the frequency domain least squares method. k The frequency response matrix G(f) at the location k Then combine G(f) at all frequency points.k The frequency response matrix G(f) of the sensor is obtained. The specific process is as follows:

[0024] G(f k )=Y(f k )·U T (f k )·[U(f k )·U T (f k )] -1

[0025] In the above formula, U(f) k )=[U1(f k ),U2(f k ),……,U M (f k )], U i (f k ) represents the time-domain excitation load sequence U i After conversion to the frequency domain, at frequency point f k The n-dimensional load column vector at the location; Y(f k )=[Y1(f k ),Y2(f k ),……,Y M (f k )], Y i (f k Y is the time-domain dynamic response load sequence. i After conversion to the frequency domain, at frequency point f k The n-dimensional response load column vector at point; i = 1, 2, ..., M; the superscript "T" indicates matrix transpose, and the superscript "-1" indicates matrix inversion; then G(f k ) is an n×n matrix.

[0026] Obtain the frequency response matrix calculation results G(f) at all frequencies k After that, extract G(f) k The element G in the i-th row and j-th column of ) ij (f k That is, the frequency f between the j-th element input and the i-th element output of the sensor. k The transfer relationship at the point; the frequency response matrix G(f) at all discrete frequency points. k ) element G ij (f k Arrange the frequencies in ascending order and concatenate them to obtain the frequency response function G of the sensor from the j-th input to the i-th output. ij (f); where, when i,j=1,2,…,n, i=j, G ij (f) is the frequency response function of the i-th element of the sensor's main channel, where G is the frequency response function when i ≠ j. ij(f) is the frequency response function of the interdimensional coupling channel from the j-th element input to the i-th element output of the sensor; all G ij (f) combine to form the frequency response function matrix G(f) of the sensor.

[0027] The advantage of this invention is that the designed hybrid excitation load table F = [F1, F1, ..., F M [A matrix] is a row orthogonal, full-rank matrix. Based on this, when performing hybrid excitation dynamic calibration experiments on multi-dimensional force sensors, it can reduce the impact of noise, especially output noise, on the frequency response estimation of the sensor. Furthermore, the calculated frequency response function G... ij The degree of noise reduction in (f) is positively correlated with the number of non-zero excitations of the j-th excitation element of the sensor in the hybrid excitation load table F, thereby improving the dynamic calibration experimental results of the multidimensional force sensor. The specific analysis is as follows:

[0028] Assume the input excitation noise of the sensor is 0, and the output noise of each element of the sensor in M ​​dynamic calibration experiments conforms to the characteristics of an ergodic random process; let the output noise of each channel of the sensor in the i-th dynamic excitation experiment be Q. i =[Q i1 Q i1 ,…,Q in ], convert it to the frequency domain to get Q i (f), then according to the least squares method, the frequency f is obtained. k The formula for calculating the frequency response matrix at point is:

[0029] G(f k )=[Y(f k )+Q(f k )]·U T (f k )·[U(f k )·U T (f k )] -1

[0030] In the above formula, Q(f) k )=[Q1(f k ),Q2(f k ),……,Q M (f k To simplify the analysis, the frequency factor f in the following analysis process is ignored. k Considering that the mixed excitation load table F is a row orthogonal, full-rank matrix, then the excitation load U is also a row orthogonal, full-rank matrix; therefore, the noise term in the frequency response estimation is...

[0031]

[0032] Suppose that in the hybrid excitation load table F, the j-th element excitation of the sensor occurs only at k...j The excitation load in the dynamic calibration experiment appeared with an amplitude of U. j ,but

[0033]

[0034] Since the noise Q conforms to the characteristics of an ergodic random process, the above equation shows that the frequency response G in the i-th row and j-th column of the frequency response matrix G(f) estimated from the hybrid excitation dynamic calibration experimental data according to the method of this invention is... ij (f) reduces the noise variance to 1 / k of the frequency response estimation noise under the unit excitation dynamic calibration condition. j That is, the noise standard deviation is reduced to the frequency response estimation noise under the condition of unit excitation dynamic calibration.

[0035] Therefore, the method of the present invention provides a simple, practical, and noise-reducing hybrid excitation dynamic calibration method for multidimensional force sensors. Attached Figure Description

[0036] Figure 1 This is a flowchart of the technical process of the method of the present invention; Detailed Implementation

[0037] The present invention will be further described below with reference to the accompanying drawings:

[0038] The design concept of this invention is as follows: Addressing the problem that estimating the sensor's frequency response function based on dynamic calibration data during hybrid excitation dynamic calibration of multi-dimensional force sensors may amplify the impact of noise, this invention starts with the construction of a hybrid excitation load table for sensor dynamic calibration. It creates a hybrid excitation load table with orthogonal rows and full rank, utilizing the orthogonal characteristic of the row vectors in the hybrid excitation load matrix to decouple noise during the frequency response function calculation process and reduce the impact of noise through averaging effects. Firstly, for the sensor and its tooling structure, excitation load direction vectors are designed according to the principle of ease of implementation. These vectors indicate the direction of the excitation load applied to the force sensor in a single dynamic calibration experiment, including hybrid excitation load direction vectors of "single force-single torque" or "single force-double torque" loading, and can also include easily implementable unit excitation load direction vectors. The "single force-single torque" hybrid excitation load direction vectors are designed in pairs, while the "single force-double torque" hybrid excitation load direction vectors are designed in groups of four, ensuring that the rows of the matrix form a matrix... The vectors are orthogonal; the total number of excitation load direction vectors is greater than or equal to the dimension of the force sensor, and the non-zero load directions should cover all measurement directions of the force sensor to ensure that the matrix they form has full row rank; secondly, load values ​​are assigned according to the excitation load direction vectors to obtain the corresponding excitation load vectors. The scale of the excitation load vectors is expanded by assigning multiple different load values ​​to each excitation load direction vector. All excitation load vectors are combined as column vectors to form a hybrid excitation load matrix, thereby constructing a hybrid excitation load table for dynamic calibration of the multidimensional force sensor; then, according to the loading requirements of each excitation load vector in the hybrid excitation load table, loading points are designed on the measuring end fixture of the sensor, and the corresponding dynamic loads are applied to the sensor in sequence according to the hybrid excitation load table to conduct dynamic calibration experiments and obtain dynamic calibration experimental data; finally, the frequency response function of each measurement channel of the sensor is calculated using the frequency domain least squares method based on all the dynamic calibration experimental data of the sensor, thereby obtaining the dynamic characteristics of the sensor.

[0039] The flowchart of the technical solution of the present invention is as follows: Figure 1 As shown, the technical process is as follows: 1. Design of excitation load direction vector → 2. Construction of hybrid excitation load table → 3. Hybrid excitation dynamic calibration experiment → 4. Calculation of frequency response function.

[0040] The excitation load direction vector design 1 refers to designing multiple direction excitation loads corresponding to different directions based on the requirements for dynamic calibration of the multi-dimensional force sensor in various directions. Where n is the dimension of the multidimensional force sensor, i.e., the number of excitation elements; the excitation elements include the force elements and torque elements measured by the force sensor; i = 1, 2, 3, ..., m, where m is the number of different excitation load direction vectors; ε i1 ε i2 ..., ε in In order to represent The corresponding excitation directions on the 1st, 2nd, ..., nth elements of the multidimensional force sensor have values ​​of 1, 0, and -1, respectively, representing positive excitation, no excitation, and negative excitation. The design follows the principle that dynamic loading of multi-dimensional force sensors is easy to implement under tooling conditions. It mainly includes mixed excitation load direction vectors of "single force-single torque" or "single force-double torque" loading, and can also include easily implemented unit excitation load direction vectors. All such excitation loads can be achieved by applying a force along a specified direction at a specified loading point on the multi-dimensional force sensor, which is easy to control.

[0041] "Single force - single moment" hybrid excitation load direction vector In this case, only one force element and its resulting torque element have an excitation direction of 1 or -1, while all other excitation elements have a direction of 0; the "single force-single torque" hybrid excitation load direction vector The design follows a one-to-two approach, meaning it designs two non-zero excitation elements with identical "single force-single moment" hybrid excitation load direction vectors. There is exactly one excitation element between the two with opposite excitation directions, thus making and The resulting matrix has orthogonal row vectors.

[0042] "Single force - dual moment" hybrid excitation load direction vector In this case, only one force element and the two torque elements it generates have an excitation direction of 1 or -1, while all other excitation elements have a direction of 0; the direction vector of the "single force-double torque" hybrid excitation load is... Based on a set of four designs, that is, designing four non-zero excitation elements with the same "single force-double moment" hybrid excitation load direction vector. and ensure The combined matrix row vectors are orthogonal; among the four mixed excitation load direction vectors, the excitation directions of the excitation elements that are not zero are preferably two positive and two negative.

[0043] Element excitation load direction vector Only one force element or torque element has an excitation direction of 1 or -1, while the other excitation elements are all 0.

[0044] All excitation load direction vectors A matrix that is a combination of column vectors should have full row rank.

[0045] Taking a six-dimensional force sensor as an example, let's assume... ε i1 ε i2 ε i3 ε i4 ε i5 ε i6The excitation directions of its six measurement elements Fx, Fy, Fz, Mx, My, and Mz are represented sequentially; where Fx, Fy, and Fz represent the force elements of the sensor along the x, y, and z coordinate axes in its coordinate system Oxyz, and Mx, My, and Mz represent the torque elements of the sensor along the x, y, and z coordinate axes in its coordinate system Oxyz. Then, by constructing multiple [elements / types] that meet the above conditions... The excitation load direction matrix F @ Example as follows:

[0046] Example 1:

[0047] Example 2:

[0048]

[0049] The matrices in the two examples above are matrices with orthogonal row vectors and full row rank.

[0050] The hybrid excitation load table construction 2 is based on the design of each excitation load direction vector. Perform load assignment to obtain the corresponding excitation load vector F i The combined excitation load table F is obtained; let L i =[l i1 ,l i2 ,...,l in ] T In response to Given the excitation load amplitude vectors of each excitation element, and the symbol "⊙" denotes vector dot product, then:

[0051] "Single force - single moment" hybrid excitation load vector pair

[0052] In the "single force-dual torque" hybrid excitation load vector group

[0053] Element excitation load vector

[0054] For each excitation load direction vector If each is configured with q different excitation load amplitude vectors L i Then we obtain M = q·m excitation load vectors F. i ; to convert all excitation load vectors F i The hybrid excitation load table F = [F1, F1, ..., F1] is obtained by combining column vectors. M], which is an n×M dimensional matrix; under the design of the excitation load direction vector design 1, F is a row orthogonal, row full-rank matrix, thus providing the prerequisite for noise decoupling and suppression when estimating the frequency response function based on the sensor hybrid excitation dynamic calibration experimental data.

[0055] Taking a six-dimensional force sensor as an example, let its six measurement directions be Fx, Fy, Fz, Mx, My, and Mz, respectively. The aforementioned two excitation load direction matrices F... @ The corresponding example of a mixed excitation load table F that conforms to row orthogonality and full row rank is as follows:

[0056] Example 1:

[0057] Example 2:

[0058]

[0059] The hybrid excitation dynamic calibration experiment 3 refers to the process of constructing each excitation load vector F in the hybrid excitation load table F based on the hybrid excitation load table construction 2. i To meet the loading requirements, a corresponding loading point P is designed on the tooling of the force sensor. i and at loading point P i The corresponding dynamic excitation load F is applied to the sensor. i Collect relevant dynamic calibration experimental data, specifically including: tooling loading point design 5, sensor dynamic excitation 6, sensor dynamic response acquisition 7.

[0060] Tooling loading point design 5: This refers to selecting or designing the tooling on the sensor's measuring end, which is related to the direction vector of the excitation load. Corresponding loading surface S i On loading surface S i Design and excitation load vector F i The corresponding loading point P i The principles are as follows:

[0061] ① Loading surface S i All perpendicular to the sensor coordinate system Oxyz and The coordinate axes are parallel to the directions of force elements whose excitation direction is not zero.

[0062] ②On the loading surface S i According to F i The magnitudes of the force element and moment element determine the loading point P. i Location;

[0063] ③As long as principles ① and ② above are met, the mixed excitation load F of group M... i The corresponding loading surface S i They are partially the same.

[0064] Sensor dynamic excitation 6: This refers to sequentially loading the sensor measuring end tooling surface S according to the hybrid excitation load table F. i Loading point P on i Apply dynamic excitation force u i This generates a corresponding dynamic excitation load F. i This was done to conduct dynamic calibration experiments on the sensor. The dynamic force was applied using either an impact method or a step method, specifically by applying force to the sensor's tooling loading surface S. i Upper P i A perpendicular line to the loading surface S is applied at the position. i The impact force or step force.

[0065] Sensor dynamic response acquisition 7: This refers to simultaneously acquiring the sensor's dynamic excitation input u while applying dynamic excitation to the sensor. i and the dynamic response output y of each measurement element i The sensor's dynamic excitation input u i That is, the applied dynamic force signal, and the dynamic response output y i The voltage signals output by each measuring element of the sensor; the number of points in the continuously acquired dynamic input and output signal sequences of the sensor is the same, N, and N must ensure that the signal has sufficient length before and after the impact or step moment and that the signals output by each element of the sensor have entered a steady state; u i Let y be a 1×N vector. i It is an n×N matrix. Based on the dynamic excitation force u... i and loading point P i The dynamic excitation load F is obtained by calculating the position coordinates. i The corresponding multidimensional excitation load sequence U i , is an n×N dimensional matrix; the dynamic response y is evaluated using the sensor's static correction coefficients. i The multidimensional dynamic response load sequence Y under dynamic excitation is obtained by making corrections. i , is an n×N dimensional matrix; i = 1, 2, ..., M.

[0066] The frequency response function calculation 4 involves calculating the frequency points f based on the input-output relationship Y(f)=G(f)U(f) of the multi-dimensional force sensor using the frequency domain least squares method. k The frequency response matrix G(f) at the location k Then combine G(f) at all frequency points. k The frequency response matrix G(f) of the sensor is obtained. The specific process is as follows:

[0067] G(f k )=Y(f k )·U T (f k )·[U(fk )·U T (f k )] -1

[0068] In the above formula, U(f) k )=[U1(f k ),U2(f k ),……,U M (f k )], U i (f k ) represents the time-domain excitation load sequence U i After conversion to the frequency domain, at frequency point f k The n-dimensional load column vector at the location; Y(f k )=[Y1(f k ),Y2(f k ),……,Y M (f k )], Y i (f k Y is the time-domain dynamic response load sequence. i After conversion to the frequency domain, at frequency point f k The n-dimensional response load column vector at point; i = 1, 2, ..., M; the superscript "T" indicates matrix transpose, and the superscript "-1" indicates matrix inversion; then G(f k ) is an n×n matrix.

[0069] Obtain the frequency response matrix calculation results G(f) at all frequencies k After that, extract G(f) k The element G in the i-th row and j-th column of ) ij (f k That is, the frequency f between the j-th element input and the i-th element output of the sensor. k The transfer relationship at the point; the frequency response matrix G(f) at all discrete frequency points. k ) element G ij (f k Arrange the frequencies in ascending order and concatenate them to obtain the frequency response function G of the sensor from the j-th input to the i-th output. ij (f); where, when i,j=1,2,…,n, i=j, G ij (f) is the frequency response function of the i-th element of the sensor's main channel, where G is the frequency response function when i ≠ j. ij (f) is the frequency response function of the interdimensional coupling channel from the j-th element input to the i-th element output of the sensor; all G ij (f) combine to form the frequency response function matrix G(f) of the sensor.

[0070] The method of this invention can reduce the impact of noise in dynamic calibration experimental data, especially output noise, on sensor frequency response estimation. Taking the hybrid excitation load table of the six-dimensional force sensor shown in Example 1 above as an example, since each element of the sensor in the hybrid excitation load table F has two sets of non-zero excitation load data, compared with 6-times unit excitation dynamic calibration, estimating the sensor frequency response based on the hybrid excitation dynamic calibration experimental data can reduce the variance of frequency response estimation noise introduced by output noise to 1 / 2 of that under unit loading dynamic calibration. Taking Example 2 above as an example, in the hybrid excitation load table F, each of the three force elements has four sets of non-zero excitation load data, while the other three torque elements each have eight sets of non-zero excitation load data. Therefore, compared to six unit excitation dynamic calibrations, estimating the sensor frequency response based on this hybrid excitation dynamic calibration experimental data can reduce the frequency response estimation noise variance of the "force input - force / torque output" channel to 1 / 4 of that under unit loading dynamic calibration, and reduce the frequency response estimation noise variance of the "torque input - force / torque output" channel to 1 / 8 of that under unit loading dynamic calibration. Repeating the experiment multiple times for each excitation load can further reduce the noise impact.

Claims

1. A method for dynamic calibration of a multidimensional force sensor using hybrid excitation to reduce noise impact. This method involves constructing a row-orthogonal, full-rank hybrid excitation load table, conducting dynamic calibration experiments on the multidimensional force sensor using hybrid excitation, obtaining hybrid excitation dynamic calibration experiment data, and calculating the sensor's frequency response function using the frequency domain least squares method to obtain the sensor's dynamic characteristics. The technical process includes: The process involves: designing the excitation load direction vector, constructing a hybrid excitation load table, conducting a hybrid excitation dynamic calibration experiment, and calculating the frequency response function. Its key features are: First, excitation load direction vectors are designed for the multi-dimensional force sensor, including hybrid excitation load direction vectors of "single force-single torque" or "single force-double torque" loading, and easily implemented unit excitation load direction vectors can also be added, ensuring that the matrix composed of all excitation load direction vectors as column vectors is orthogonal and has full rank. Second, load values ​​are assigned according to the excitation load direction vectors to obtain the corresponding excitation load vectors. The scale of the excitation load vectors is expanded by assigning multiple different load values ​​to each excitation load direction vector, and all excitation load vectors are combined as column vectors to form a hybrid excitation load matrix, thereby constructing a hybrid excitation load table for the dynamic calibration of the multi-dimensional force sensor. Then, according to the loading requirements of each excitation load vector in the hybrid excitation load table, loading points are designed on the sensor's measuring end fixture, and the corresponding dynamic loads are applied to the sensor sequentially according to the hybrid excitation load table to conduct dynamic calibration experiments and obtain dynamic calibration experimental data. Finally, based on all the dynamic calibration experimental data of the sensor, the frequency response function of each measurement channel of the sensor is calculated using the frequency domain least squares method, thereby obtaining the dynamic characteristics of the sensor.

2. The method for dynamic calibration of a multi-dimensional force sensor with hybrid excitation to reduce noise impact as described in claim 1, characterized in that: Excitation load direction vector design refers to designing direction vectors corresponding to excitation loads in multiple different directions based on the requirements for dynamic calibration of multi-dimensional force sensors in various directions. Where n is the dimension of the multidimensional force sensor, that is, the number of excitation elements; the excitation elements include each measured force element and torque element of the force sensor; i = 1, 2, 3, ..., m, where m is the number of different excitation load direction vectors; , ... In order to represent The corresponding excitation directions on the 1st, 2nd, ..., nth elements of the multidimensional force sensor have values ​​of 1, 0, and -1, representing positive excitation, no excitation, and negative excitation, respectively. The design follows the principle that dynamic loading of multi-dimensional force sensors is easy to implement under tooling conditions. It mainly includes the direction vector of mixed excitation loads of "single force-single torque" or "single force-double torque" loading, and can also include the direction vector of unit excitation loads that are easy to implement. All such excitation loads can be achieved by applying a force along a specified direction at a specified loading point on the multi-dimensional force sensor, which is easy to control. "Single force - single moment" hybrid excitation load direction vector In this case, only one force element and its resulting torque element have an excitation direction of 1 or -1, while all other excitation elements have a direction of 0; the "single force-single torque" hybrid excitation load direction vector The design follows a one-to-two approach, meaning it designs two non-zero excitation elements with identical "single force-single moment" hybrid excitation load direction vectors. , There is one and only one excitation element between the two with opposite excitation directions, thus making and The resulting matrix has orthogonal row vectors; "Single force-dual moment" hybrid excitation load direction vector In this case, only one force element and the two torque elements it causes have an excitation direction of 1 or -1, while all other excitation elements have a direction of 0; the "single force-double torque" hybrid excitation load direction vector Based on a set of four designs, that is, designing four non-zero excitation elements with the same "single force-double moment" hybrid excitation load direction vector. , , , and ensure , , , The row vectors of the combined matrix are orthogonal; Element excitation load direction vector Only one force element or torque element has an excitation direction of 1 or -1, while the other excitation elements have an excitation direction of 0. All excitation load direction vectors A matrix that is a combination of column vectors should have full row rank.

3. The method for dynamic calibration of a multi-dimensional force sensor with hybrid excitation to reduce noise impact as described in claim 1, characterized in that: The construction of the hybrid excitation load table is based on the various excitation load direction vectors in the design. Perform load assignment to obtain the corresponding excitation load vector. The combined excitation load table is obtained. ;set up In response to The excitation load amplitude vector of each excitation element, symbol " " represents the dot product of vectors, then: "Single force - single moment" hybrid excitation load vector pair , ; In the "single force-dual torque" hybrid excitation load vector group , , , ; Element excitation load vector ; For each excitation load direction vector If each is configured with q different excitation load amplitude vectors Then obtain Excitation load vector ; to convert all excitation load vectors The hybrid excitation load table is obtained by combining column vectors. It is an n×M dimensional matrix; It is a row orthogonal, full-rank matrix, which provides the prerequisite for noise decoupling and suppression when estimating the frequency response function based on the experimental data of dynamic calibration of sensor hybrid excitation.

4. The method for dynamic calibration of a multi-dimensional force sensor with hybrid excitation to reduce noise impact as described in claim 1, characterized in that: The hybrid excitation dynamic calibration experiment is based on the constructed hybrid excitation load table. Each excitation load vector To meet the loading requirements, corresponding loading points should be designed on the tooling of the force sensor. and at the loading point The corresponding dynamic excitation load is applied to the sensor. Collect relevant dynamic calibration experimental data, including: tooling loading point design, sensor dynamic excitation, and sensor dynamic response acquisition. Tooling loading point design: This refers to selecting or designing the tooling on the sensor's measuring end that is aligned with the direction vector of the excitation load. Corresponding loading surface On the loading surface Design and excitation load vector The corresponding loading point P i The principles are as follows: Loading surface S i All perpendicular to the sensor coordinate system Oxyz and The coordinate axes are parallel to the directions of force elements whose excitation direction is not zero. On loading surface S i According to The magnitudes of the force element and moment element determine the loading point P. i Location; As long as the above principles are met and M group of mixed excitation loads The corresponding loading surface S i The functions are partially the same; Sensor dynamic excitation: This refers to sequentially loading the sensor's measuring end tooling surface S according to the hybrid excitation load table F. i Loading point P on i Apply dynamic excitation force u i This generates a corresponding dynamic excitation load. To conduct dynamic calibration experiments on the sensor; the dynamic force is applied using either the impact method or the step method, i.e., on the tooling loading surface S of the sensor. i Upper P i A perpendicular line to the loading surface S is applied at the position. i Impact force or step force; Sensor dynamic response acquisition: This refers to simultaneously acquiring the sensor's dynamic excitation input u while applying dynamic excitation to the sensor. i and the dynamic response output y of each measurement element i The dynamic excitation input u of the sensor i That is, the applied dynamic force signal, and the dynamic response output y i The voltage signals output by each measuring element of the sensor; the number of points in the continuously acquired dynamic input and output signal sequences of the sensor is the same, N, and N must ensure that the signal has sufficient length before and after the impact or step moment and that the signals output by each element of the sensor have entered a steady state; u i Let y be a 1×N vector. i It is an n×N matrix; based on the dynamic excitation force u i and loading point P i The position coordinates are used to calculate the dynamic excitation load. Corresponding multidimensional excitation load sequence , is an n×N dimensional matrix; the dynamic response y is evaluated using the sensor's static correction coefficients. i The multidimensional dynamic response load sequence under dynamic excitation is obtained by making corrections. , is an n×N dimensional matrix; i = 1, 2, …, M.

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