摘 要：对光栅尺测量系统中各种干扰因素进行了研究，提出了基于互补集合经验模态分解（CEEMD）主成分分析（PCA）的测量误差补偿方法，以提高光栅尺测量精度。对光测量误差进行 CEEMD 分解获取一系列固有模态分量（IMF），各分量进行PCA 并计算主成分个数所对应 IMF 分量的贡献率，选取合适的 IMF 分量作为测量误差趋势以提高测量精度。从实验结果上看，所提出误差补偿方法的均方根误差为 0.518 μm，置信区间为（-0.099，0.010 6），验证了这种方法的有效性和可行性。
关键词：互补集合经验模态分解；主成分分析；误差补偿
DOI:10.19850/j.cnki.2096-4706.2021.10.041
中图分类号：TP212 文献标识码：A 文章编号：2096-4706（2021）10-0155-04
Measurement Error Compensation Based on CEEMD Principal Component Analysis
LI Wenjian
（Guangdong University of Technology，Guangzhou 510006，China）
Abstract：Various interference factors in the grating ruler measurement system are studied，and a measurement error compensation method based on complementary ensemble empirical mode decomposition（CEEMD）and principal component analysis（PCA）is proposed to improve the measurement accuracy of grating ruler. The optical measurement error is carried out CEEMD decomposition to obtain a series of intrinsic mode function（IMF）. PCA is performed for each component，the contribution rate of IMF component corresponding to the number of principal components is calculated，and the appropriate IMF component is selected as the measurement error trend to improve the measurement accuracy. According to the experimental results，the root mean squared error of the proposed error compensation method is 0.518 μm，and the confidence interval is（-0.099，0.010 6），which verifies the effectiveness and feasibility of this method.
Keywords：complementary ensemble empirical mode decomposition；principal component analysis；error compensation
参考文献：
[1] PENG D L，FU M，CHEN X H，et al. Classification Study on Typical Displacement Sensors and Analysis on the Characteristics of Time Grating Sensors [J].Journal of Mechanical Engineering，2018，54 （10）：36.
[2] BARAKAUSKAS A，BARAUSKAS R，KASPARAITIS A，et al. Error modelling of optical encoders based on Moiré effect [J]. Journal of Vibroengineering，2017，19（1）：38-48.
[3] HU F，CHEN X D，CAI N，et al. Error analysis and compensation of an optical linear encoder [J].IET Science，Measurement & Technology，2018，12（4）：561-566.
[4] GURAUSKIS D，KILIKEVIČIUS A. Dynamic Behaviour Analysis of Optical Linear Encoder under Mechanical Vibrations [J]. Mechanika，2020，26（1）：35-41.
[5] CAI N，XIAO P，YE Q，et al. Improving the measurement accuracy of an absolute imaging position encoder via a new edge detection method [J].IET Science， Measurement & Technology，2017，11（4）：406-413.
[6] CHENG X，MAO J D，LI J，et al. An EEMD-SVD-LWT algorithm for denoising a lidar signal [J/OL].Measurement，2021， 168：[2021-03-24].https://doi.org/10.1016/j.measurement.2020.108405.
[7] QIAO Y，LI Q，QIAN H D，et al. Seismic signal denoising method based on CEEMD and improved wavelet threshold [J].IOP Conference Series：Earth and Environmental Science，2021，671（1）： 012036.
[8] 聂振国，赵学智 .PCA 与 SVD 信号处理效果相似性与机 理分析 [J]. 振动与冲击，2016，35（2）：12-17.
[9] WANG H，WANG J，CHEN B，et al. Absolute optical imaging position encoder [J].Measurement，2015，67：42-50.
作者简介：李文剑（1995.10—），男，汉族，广东清远人， 硕士研究生，研究方向：信号处理。