Article

Measuring displacement signal with an accelerometer

Journal of Mechanical Science and Technology (Impact Factor: 0.84). 06/2010; 24(6):1329-1335. DOI: 10.1007/s12206-010-0336-1

ABSTRACT

An effective and simple way to reconstruct displacement signal from a measured acceleration signal is proposed in this paper.
To reconstruct displacement signal by means of double-integrating the time domain acceleration signal, the Nyquist frequency
of the digital sampling of the acceleration signal should be much higher than the highest frequency component of the signal.
On the other hand, to reconstruct displacement signal by taking the inverse Fourier transform, the magnitude of the significant
frequency components of the Fourier transform of the acceleration signal should be greater than the 6 dB increment line along
the frequency axis. With a predetermined resolution in time and frequency domain, determined by the sampling rate to measure
and record the original signal, reconstructing high-frequency signals in the time domain and reconstructing low-frequency
signals in the frequency domain will produce biased errors. Furthermore, because of the DC components inevitably included
in the sampling process, low-frequency components of the signals are overestimated when displacement signals are reconstructed
from the Fourier transform of the acceleration signal. The proposed method utilizes curve-fitting around the significant frequency
components of the Fourier transform of the acceleration signal before it is inverse-Fourier transformed. Curve-fitting around
the dominant frequency components provides much better results than simply ignoring the insignificant frequency components
of the signal.

KeywordsAcceleration signal-Curve-fitting-Displacement signal-Inverse Fourier transform-Nyquist frequency-Sampling rate

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    • "Determining relative displacements can be accomplished by several methodologies. The most common method is the double integration of the acceleration by a rectangular or trapezoidal rule (Sangbo, 2010). Generally, this problem can be described by the formula "
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    • "In the process, the frequency components that are deemed unnecessary can be discarded. If the acceleration signals display several distinct frequency components as in the case of modal testing, the frequency domain method using curve-fitting technique produces excellent results [14]. If the acceleration signal has a broad spectrum, however, it is difficult to apply the curve-fitting method. "
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