基于矢量分解原理的三轴加速度计同步冲击标定方法

王清华; 张媛媛; 高猛; 徐丰; 郭伟国

doi:10.11883/bzycj-2023-0007

基于矢量分解原理的三轴加速度计同步冲击标定方法

doi: 10.11883/bzycj-2023-0007

王清华^1,,
张媛媛²,
高猛¹,
徐丰²,
郭伟国^1, ,

1.
西北工业大学航空学院，陕西西安 710072
2.
西北工业大学航天学院，陕西西安 710072

基金项目: 国家自然科学基金（11872051）

详细信息

作者简介:
王清华（1993－　），男，博士研究生，QinghuaWang@mail.nwpu.edu.cn

通讯作者:
郭伟国（1960－　），男，博士，教授，weiguo@nwpu.edu.cn

中图分类号: O347
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- 被引次数: 0
出版历程
- 收稿日期: 2023-01-05
- 修回日期: 2023-04-19
- 网络出版日期: 2023-05-05
- 刊出日期: 2023-07-05

A method for synchronous shock calibration of triaxial accelerometers based on vector decomposition

1.
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China
2.
School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China

摘要

摘要: 如何沿空间三坐标轴方向激励能够被准确追溯和计量的三分量同步冲击载荷是三轴加速度计标定技术中的核心和关键。为实现对大量程（10²g～10⁴g）三轴加速度计的同步冲击标定，采用跌落台配合冲击放大器激励沿竖直方向的单轴冲击载荷，借助设置有倾斜面的砧座并基于矢量分解原理，将沿竖直方向激励的单轴冲击载荷分解到以特定姿态安装的三轴加速度计的各敏感轴上，以此实现了三分量冲击载荷的同步激励与三轴加速度计的同步冲击加载。采用高速相机结合MATLAB图像处理的方法，对冲击标定过程中三轴加速度计各敏感轴输入的加速度进行了计量。基于最小二乘原理与矩阵微分，对同步标定中三轴加速度计包含主灵敏度系数与轴间耦合灵敏度系数的灵敏度矩阵进行了求解。对单轴依次标定和同步标定后三轴加速度计的泛化测量精度进行了对比。研究结果表明：采用基于矢量分解原理的同步冲击载荷激励方法可实现对三轴加速度计各敏感轴的同步冲击加载；基于高速相机与MATLAB图像处理的测量方法作为一种绝对光学测量法应用于加速度计冲击标定中，对加速度的测量具有可行性和有效性；同步标定相对单轴依次标定可提升三轴加速度计的测量精度，实际工程中，对三轴加速度计建议选用同步法进行标定，以保证测量结果的准确性和可靠性。
- 加速度计 /
- 标定 /
- 三轴同步 /
- 图像处理 /
- 跌落台 /
- 冲击放大器
Abstract: The triaxial accelerometer can simultaneously detect and measure shock loads along the three coordinate axes in the three-dimensional space. Therefore, it has a wide range of applications in the fields of spatial vibration test, spatial impact test, and so on. Before being put into practical use, triaxial accelerometers must be calibrated for their sensitivity coefficients to ensure the validity and accuracy of measurements. Unlike the calibration of single-axis accelerometers, there is a major difficulty in the calibration technologies of the triaxial accelerometers, that is, how to realize the excitation of three-dimensional shock loads synchronously, since the pulse width of the shock loads are usually as short as a few milliseconds. On the other hand, tracing and measuring the acceleration excited during shock process is also the key to the shock calibration of accelerometers. In order to address the aforementioned problems, a drop table equipped with a shock amplifier was used to excite acceleration loads vertically upward. Then, with the help of an anvil which has a bevel, the vertical acceleration excited on shock amplifier was decomposed to each sensitive axis of the triaxial accelerometer based the principle of vector decomposition. By means of this approach, synchronous shock loading of the triaxial accelerometer was then realized. High-speed camera and image processing based on MATLAB were used to trace and measure the acceleration excited in the synchronous shock calibration of triaxial accelerometers. Experiments were conducted to verify the effectiveness of the motion measurement method based on high-speed camera and MATLAB image processing. The sensitivity matrix of the triaxial accelerometer, which takes into consideration both the main sensitivity coefficients and the coupling sensitivity coefficients, was solved using the least-square method. At last, the measurement accuracy of the accelerometer calibrated using the synchronous method was compared with the measurement accuracy of the accelerometer calibrated using the conventional asynchronous method. The research results indicate that the conventional drop table could excite a wide range (10²g~10⁴g) of acceleration by equipping a shock amplifier. In addition, the motion measurement method based on high-speed camera and MATLAB image processing is valid in acceleration traceability or measurement in the shock calibration of accelerometer. Furthermore, compared to the measurement accuracy of the accelerometer calibrated by the asynchronous method, the measurement accuracy of the triaxial accelerometer could be guaranteed and improved by using the synchronous method. Therefore, in engineering, the triaxial accelerometer ought to be calibrated using synchronous methods rather than asynchronous methods to guarantee the validity and accuracy of measurements.
- accelerometer /
- calibration /
- three-axis synchronization /
- image processing /
- drop table /
- impact amplifier

HTML全文

图 1 基于跌落台与冲击放大器的三轴加速度计同步冲击标定装置示意图

Figure 1. Schematic diagram of the synchronous shock calibration device for a triaxial accelerometer based on a drop table and a shock amplifier

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图 2 三轴加速度计同步冲击加载原理图

Figure 2. Schematic diagram of the syncchronous shock loading of a triaxial accelerometer

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图 3 基于高速摄像机与MATLAB图像处理的加速度测量原理

Figure 3. Schematic diagram of acceleration measurement based on a high-speed camera and MATLAB image processing

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图 4 基于高速相机与MATLAB图像处理的加速度测量有效性测试实验设置

Figure 4. Experimental setup for validity test of acceleration measurement method based on high-speed camera and MATLAB image processing

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图 5 高速摄像机视场

Figure 5. Field of view of high-speed camera

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图 6 MATLAB程序运行效果图

Figure 6. Rendering of MATLAB program running

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图 7 获取标记点中心处像素值

Figure 7. Obtainment of the pixel valueat the center of the marker point

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图 8 待标定三轴加速度计

Figure 8. Triaxial accelerometer to be calibrated

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图 9 单轴依次标定中三轴加速度计的安装姿态

Figure 9. Mounting attitude of the triaxial accelerometer in sequential calibration for each sensitive axis

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图 10 同步标定中加速度计的安装过程

Figure 10. Installation of the accelerometer in synchronous calibration

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图 11 典型锤头位移-时间曲线及数据处理方法

Figure 11. Typical displacement-time curve of the hammer and the method of data processing

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图 12 标准加速度计信号与相应MATLAB图像处理所得加速度信号对比

Figure 12. Signal comparison between reference accelerometer and MATLAB image processing

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图 13 三轴同步冲击标定的典型原始数据

Figure 13. Typical original data obtained by three-axis synchronous shock calibration

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图 14 单轴依次标定加速度计测量结果$ {a}_{\mathrm{s}\mathrm{e}\mathrm{q}} $与同步标定加速度计测量结果$ {a}_{\mathrm{s}\mathrm{y}\mathrm{n}} $相对加速度输入$ {a}_{\mathrm{i}\mathrm{p}\mathrm{t}} $的误差及对比

Figure 14. Error and its comparison of $ {a}_{\mathrm{s}\mathrm{e}\mathrm{q}} $ which output from the accelerometer calibrated with sequential method and $ {a}_{\mathrm{s}\mathrm{y}\mathrm{n}} $ which output from the accelerometer calibrated with synchronous method relative to acceleration input $ {a}_{\mathrm{i}\mathrm{p}\mathrm{t}} $

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表 1 加速度计输出信号与MATLAB图像处理所得测量信号幅值对比

Table 1. Amplitude comparison between accelerometer output and MATLAB image processing

序号	加速度计	MATLAB	相对误差/%
测试1	998g	996g	0.20
测试2	2134g	2128g	0.28
测试3	9987g	9903g	0.84

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表 2 单轴依次标定所得三轴加速度计主灵敏度系数

Table 2. Main sensitivity coefficients of the triaxial accelerometer obtain from sequential calibration

灵敏度系数/(pC·m⁻¹·s²)	S_xx	S_yy	S_zz
数值	0.442	0.435	0.452

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表 3 同步标定所得三轴加速度计主灵敏度系数与轴间耦合灵敏度系数

Table 3. Main and coupling sensitivity coefficients of the triaxial accelerometer obtain from synchronous calibration

灵敏度系数/(pC·m⁻¹·s²)	S_xx	S_xy	S_xz	S_yx	S_yy	S_yz	S_zx	S_zy	S_zz
数值	0.414	0.016 4	−0.007 5	−0.012 9	0.427	0.013 5	−0.014 5	−0.011	0.441

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表 4 验证实验工况及单轴依次标定与同步标定后加速度计的测量值

Table 4. Conditions of the validation experiments and outputs of the accelerometer calibrated with sequential and synchronous method, respectively

序号	工况	敏感轴	a_ipt/g	a_seq/g	a_syn/g
实验1	a_ref=958g， α=30°，β=30°	x	239.5	227.8	241.9
		y	414.8	428.0	416.9
		z	829.7	799.8	838.1
实验2	a_ref=1624g， α=30°，β=60°	x	703.2	655.8	709.7
		y	406.0	426.2	410.6
		z	1406.4	1355.2	1422.5
实验3	a_ref=2897g， α=55°，β=45°	x	1678.0	1617.5	1690.6
		y	1678.0	1657.8	1686.7
		z	1661.7	1547.6	1683.9
注：(1) a_ipt为根据式(2)计算得到的加速度计各敏感轴的输入值。(2) a_seq为单轴依次标定加速度计的测量值。(3) a_syn为同步标定加速度计的测量值。

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参考文献(29)

[1]	周露, 宋浩兰, 白静蕾, 等. 基于三轴加速度计和SVM算法的校园运动识别 [J]. 电子设计工程, 2022, 30(21): 80–84. DOI: 10.14022/j.issn1674-6236.2022.21.017. ZHOU L, SONG H L, BAI J L, et al. Campus movement recognition based on three-axis accelerometer and SVM algorithm [J]. Electronic Design Engineering, 2022, 30(21): 80–84. DOI: 10.14022/j.issn1674-6236.2022.21.017.
[2]	高鹏, 杨硕, 高勇, 等. 基于三轴加速度计的振动筛运动状态采集装置的设计 [J]. 选煤技术, 2021(2): 88–92. DOI: 10.16447/j.cnki.cpt.2021.02.017. GAO P, YANG S, GAO Y, et al. Design of the 3-axis accelerometer-based vibrating screen motion state information acquisition device [J]. Coal Preparation Technology, 2021(2): 88–92. DOI: 10.16447/j.cnki.cpt.2021.02.017.
[3]	何青, 杜冬梅, 张志, 等. 三轴加速度计在水下结构振动测试中的应用 [J]. 微纳电子技术, 2007, 44(7): 159–161. DOI: 10.13250/j.cnki.wndz.2007.z1.044. HE Q, DU D M, ZHANG Z, et al. Application of vibration measurement for underwater structure [J]. Micronanoelectronic Technology, 2007, 44(7): 159–161. DOI: 10.13250/j.cnki.wndz.2007.z1.044.
[4]	高婵, 杜国平. 基于三轴加速度计的桥涵防碰撞报警装置的设计 [J]. 传感技术学报, 2014, 27(9): 1178–1182. GAO C, DU G P. Design of bridges and culverts anti-collision alarm device based on three-axis accelerometer [J]. Chinese Journal of Sensors and Actuators, 2014, 27(9): 1178–1182.
[5]	范成叶, 李杰, 景增增, 等. 旋转弹用三轴加速度计安装位置误差标定补偿技术 [J]. 传感技术学报, 2013, 26(10): 1352–1356. DOI: 10.3969/j.issn.1004-1699.2013.10.007. FAN C Y, LI J, JING Z Z, et al. Calibration and compensation method on installation position error of tri-axis accelerometer units used in spinning projectiles [J]. Chinese Journal of Sensors and Actuators, 2013, 26(10): 1352–1356. DOI: 10.3969/j.issn.1004-1699.2013.10.007.
[6]	黎渊, 董培涛, 吴学忠, 等. 三轴高g加速度计的测试方法及实验研究 [J]. 传感技术学报, 2008, 21(11): 1844–1847. DOI: 10.3969/j.issn.1004-1699.2008.11.007. LI Y, DONG P T, WU X Z, et al. Study on characterization of a triaxial high-g accelerometer [J]. Chinese Journal of Sensors and Actuators, 2008, 21(11): 1844–1847. DOI: 10.3969/j.issn.1004-1699.2008.11.007.
[7]	RIPPER G P, DIAS R S, GARCIA G A. Primary accelerometer calibration problems due to vibration exciters [J]. Measurement, 2009, 42(9): 1363–1369. DOI: 10.1016/j.measurement.2009.05.002.
[8]	OOTA A, USUDA T, NOZATO H. Correction and evaluation of the effect due to parasitic motion on primary accelerometer calibration [J]. Measurement, 2010, 43(5): 719–725. DOI: 10.1016/j.measurement.2010.02.005.
[9]	陈德英, 茅盘松, 张旭, 等. 一种压阻式高g值加速度传感器 [J]. 固体电子学研究与进展, 2004, 24(3): 318–321, 349. DOI: 10.3969/j.issn.1000-3819.2004.03.010. CHEN D Y, MAO P S, ZHANG X, et al. A piezoresistive accelerometer with high-g value [J]. Research & Process of SSE, 2004, 24(3): 318–321, 349. DOI: 10.3969/j.issn.1000-3819.2004.03.010.
[10]	李玉龙, 郭伟国, 贾德新, 等. 高g 值加速度传感器校准系统的研究 [J]. 爆炸与冲击, 1997, 17(1): 90–96. LI Y L, GUO W G, JIA D X, et al. An equipment for calibrating high shock acceleration sensors [J]. Explosion and Shock Waves, 1997, 17(1): 90–96.
[11]	李功, 焦新泉, 袁强. MEMS高g值复合量程开关设计 [J]. 传感器与微系统, 2016, 35(1): 82–84, 87. DOI: 10.13873/J.1000-9787(2016)01-0082-03. LI G, JIAO X Q, YUAN Q. Design of MEMS high-g composite range switch [J]. Transducer and Microsystem Technologies, 2016, 35(1): 82–84, 87. DOI: 10.13873/J.1000-9787(2016)01-0082-03.
[12]	YUAN K B, GUO W G, SU Y, et al. Study on several key problems in shock calibration of high-g accelerometers using Hopkinson bar [J]. Sensors and Actuators A: Physical, 2017, 258: 1–13. DOI: 10.1016/j.sna.2017.02.017.
[13]	WON S H P, GOLNARAGHI F. A triaxial accelerometer calibration method using a mathematical model [J]. IEEE Transactions on Instrumentation and Measurement, 2010, 59(8): 2144–2153. DOI: 10.1109/TIM.2009.2031849.
[14]	SIPOS M, PACES P, ROHAC J, et al. Analyses of triaxial accelerometer calibration algorithms [J]. IEEE Sensors Journal, 2012, 12(5): 1157–1165. DOI: 10.1109/JSEN.2011.2167319.
[15]	BERAVS T, PODOBNIK J, MUNIH M. Three-axial accelerometer calibration using Kalman filter covariance matrix for online estimation of optimal sensor orientation [J]. IEEE Transactions on Instrumentation and Measurement, 2012, 61(9): 2501–2511. DOI: 10.1109/TIM.2012.2187360.
[16]	UMEDA A, ONOE M, SAKATA K, et al. Calibration of three-axis accelerometers using a three-dimensional vibration generator and three laser interferometers [J]. Sensors & Actuators A: Physical, 2004, 114(1): 93–101. DOI: 10.1016/j.sna.2004.03.011.
[17]	张俊, 熊晓燕, 姚爱英. 可调节式三轴标定台和解耦的设计与研究 [J]. 机床与液压, 2017, 45(3): 159–162. DOI: 10.3969/j.issn.1001-3881.2017.03.036. ZHANG J, XIONG X Y, YAO A Y, et al. Design and research on an adjustable three axis calibration and decoupling [J]. Machine Tool & Hydraulics, 2017, 45(3): 159–162. DOI: 10.3969/j.issn.1001-3881.2017.03.036.
[18]	曾国英, 刘继光, 夏季. 三维振动台的仿真设计 [J]. 机械设计, 2005, 22(4): 46–48. DOI: 10.13841/j.cnki.jxsj.2005.04.016. ZENG G Y, LIU J G, XIA J. Emulation design of 3D vibration table [J]. Journal of Machine Design, 2005, 22(4): 46–48. DOI: 10.13841/j.cnki.jxsj.2005.04.016.
[19]	郑建洲, 武元桢. 平面静压式传振解耦装置及三轴向振动复合试验台: CN102865987B [P]. 2015-01-07.
[20]	ISO. Methods for the calibration of vibration and shock transducers: Part 11: primary vibration calibration by laser interferometry: ISO16063-11 [S]. 1999.
[21]	ISO. Methods for the calibration of vibration and shock transducers: Part 13: primary shock calibration using laser interferometry: ISO 16063-13 [S]. 2001.
[22]	YUE Z W, SONG Y, LI P H, et al. Applications of digital image correlation (DIC) and the strain gage method for measuring dynamic mode Ⅰ fracture parameters of the white marble specimen [J]. Rock Mechanics and Rock Engineering, 2019, 52: 4203–4216. DOI: 10.1007/s00603-019-01830-8.
[23]	GAO G, YAO W, XIA K, et al. Investigation of the rate dependence of fracture propagation in rocks using digital image correlation (DIC) method [J]. Engineering Fracture Mechanics, 2015, 138: 146–155. DOI: 10.1016/j.engfracmech.2015.02.021.
[24]	XING H Z, WANG M Y, JU M H, et al. Measurement of ejection velocity of rock fragments under dynamic compression and insight into energy partitioning [J]. International Journal of Rock Mechanics and Mining Sciences, 2022, 149: 104992. DOI: 10.1016/j.ijrmms.2021.104992.
[25]	余旭东, 吴斌, 徐超, 等. 飞行器结构动力学[M]. 西安: 西北工业大学出版社, 2012: 19–48.
[26]	BELKHOUCHE F. Robust calibration of MEMS accelerometers in the presence of outliers [J]. IEEE Sensors Journal, 2022, 22(10): 9500–9508. DOI: 10.1109/JSEN.2022.3163964.
[27]	WANG Q H, XU F, GUO W G, et al. New technique for impact calibration of wide-range triaxial force transducer using Hopkinson bar [J]. Sensors, 2022, 22(13): 4885.DOI. DOI: 10.3390/s22134885.
[28]	CHEN X Y, ZHANG X T, ZHU M, et al. A novel calibration method for tri-axial magnetometers based on an expanded error model and a two-step total least square algorithm [J]. Mobile Networks and Applications, 2022, 27(2): 794–805. DOI: 10.1007/s11036-021-01898-z.
[29]	ISO. Methods for the calibration of vibration and shock transducers: Part 22: shock calibration by comparison to a reference transducer: amendment 1: ISO 16063-22:2005/Amd 1 [S]. 2014.