Precise sinusoidal signal extraction from noisy waveform in vibration calibration

Abstract

Precise extraction of sinusoidal vibration parameters is essential for the dynamic calibration of vibration sensors, such as accelerometers. However, several standard methods have not yet been optimized for large background noise. In this work, signal processing methods to extract small vibration signals from noisy data in the case of accelerometer calibration are discussed. The results show that spectral leakage degrades calibration accuracy. Three methods based on the use of a filter, window function, and numerical differentiation are investigated to reduce the contribution of the calibration system noise. We demonstrate the effectiveness of these methods with theoretical calculations, simulations, and experiments. The uncertainty of microvibration calibration in the National Metrology Institute of Japan is reduced by two orders of magnitudes using the proposed methods. We recommend to use a combination of numerical differentiation and either a time-domain window function or a bandpass filter for most accelerometer microvibration sensitivity calibrations. For suppressing the effects of line noise, adjusting the data set length is also effective.

Investigation of sound pressure leakage effect for primary calibration down to 10−2 Hz using a laser pistonphone system

“…To reduce the uncertainty associated with fitting, the data length was adjusted to n/f (n: an integer greater than or equal to 10), and the Hanning window was applied to each signal [29]. The experimental data from 0.04 Hz to 2 Hz were extracted and used for evaluation because the S/N ratio deteriorated at lower frequencies and the high-pass frequency response of the pressure sensor might affect the analysis at higher frequencies.…”

Primary microvibration standards down to 10−3 m s−2 at low frequency

“…In the proposed system, the interferometer signal is first numerically differentiated twice to convert the displacement signal to acceleration, a IF , so as to compare the AUT and interferometer signals in the same quantity. Then, the Hanning window is multiplied by V AUT and a IF before SAM [20]. After SAM, the magnitude, S cal , and phase shift, ∆ϕ cal , of the complex sensitivity of the AUT are calculated as…”

“…Note that systematic bias is not considered here because we assumed that the random error terms distributed around zero. As discussed in [20], the uncertainty due to random noise is the same for the phase shift, i.e. u noise,ϕ (∆ϕ cal ) = u noise (S cal )/S cal .…”

“…For microvibration calibration, we adopted signal preprocessing using a numerical differentiation and the Hanning window, as explained above. These preprocesses minimized the background noise contributions through the spectral leakage from frequencies other than f v [20]. As a result, the standard deviation of the noise amplitude was determined by the noise spectrum at…”

“…With the decrease in calibration input vibration amplitudes, their contribution becomes relatively significant. Recently, aiming at reducing the uncertainties in microvibration calibration systems, we reported a noise reduction method for a lowfrequency calibration system [19], as well as a method for the modification of signal processing [20]. In this study, we combined these results and constructed a calibration system that is compatible with the calibration of both large vibrations (10 m s −2 ) and microvibrations (10 −3 m s −2 ).…”