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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 2759092, 9 pages
Research Article

Denoising and Trend Terms Elimination Algorithm of Accelerometer Signals

School of Electric and Information Engineer, Zhongyuan University of Technology, Zhengzhou 450007, China

Received 22 December 2015; Accepted 30 March 2016

Academic Editor: Mingcong Deng

Copyright © 2016 Peng Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Acceleration-based displacement measurement approach is often used to measure the polish rod displacement in the oilfield pumping well. Random noises and trend terms of the accelerometer signals are the main factors that affect the measuring accuracy. In this paper, an efficient online learning algorithm is proposed to improve the measurement precision of polish rod displacement in the oilfield pumping well. To remove the random noises and eliminate the trend term of accelerometer signals, the ARIMA model and its parameters are firstly derived by using the obtained data of time series of acceleration sensor signals. Secondly, the period of the accelerometer signals is estimated through the Rife-Jane frequency estimation approach based on Fast Fourier Transform. With the obtained model and parameters, the random noises are removed by employing the Kalman filtering algorithm. The quadratic integration of the period is calculated to obtain the polish rod displacement. Moreover, the windowed recursive least squares algorithm is implemented to eliminate the trend terms. The simulation results demonstrate that the proposed online learning algorithm is able to remove the random noises and trend terms effectively and greatly improves the measurement accuracy of the displacement.