Cancellation of parametric-effect-induced error in airborne ultrasound Doppler velocimetry

Abstract

A non-contact vibration measuring technique based on ultrasonic Doppler effect is studied. Two effects induce phase modulation on the received ultrasound signal, which are Doppler effect and nonlinear parametric effect. With the increasing of vibrating frequency, the phase variation due to parametric effect is getting greater and greater. In this paper, by measuring the acoustic pressure generated by the low frequency vibration, the parametric effect is taken into account for estimating the vibrating velocity. The results show that it is better than the method of only taking account of the Doppler effect especially as the vibrating frequency increases. For example, for a vibrating body of diameter 10 cm at frequency of 1.5 kHz, the error of velocity measurement with parametric-effect-compensation is getting less than one half of that without compensation.

Vibration parameter estimation methods for ultrasonic measurement systems – a review

“…A series of advantages using Gaussian beam function to define the beam field of an axis symmetric acoustical radiator could be found in [27] and applied in defining the scattering of sound by sound [68]. The combined effect of Doppler and parametric [23,24] have been applied on vibration measurement applications [21][22][23][24][25][26].…”

“…However, the low-frequency acoustic wave emitted by a small vibrating body is not a plane wave. In fact, the plane wave assumption is no longer valid [26]. Normally, because of the finite size of transducer, diffraction effect occurs at the source that could be the error in plane wave assumption.…”

“…(7) Parametric interaction: The phase shift of parametric effect is proportional to the low-frequency pressure and vibration speed. This phase shift need to be cancelled from Doppler vibration measurement to obtain higher accuracy [21][22][23][24][25][26]. (8) Quasi-stationary approximation: Doppler effect assumes the quasi-stationary approximation, which means scattering field by a moving surface is to be considered as stationary field as if the surface was frozen at that time [24].…”

“…Similarly, the spatial resolution in the estimation of object displacement is achieved in less than several micrometres using least square technique [13] compared with the correlation techniques [9]. The methods listed in Table 1 measure the vibration signal information using Doppler effect by neglecting the parametric effect except the PLL technique [26]. Table 2 lists the various procedures that utilise only the Doppler effect, Doppler and parametric effects.…”

“…In these methods the vibration signal information is obtained through measuring the phase shift, time delay, Doppler frequency etc. In combined Doppler and parametric effects, few procedures try to cancel out the parametric effect by placing the microphone in between the transmitter and receiver at some distance [26]. If the parametric effect is considered for extracting the vibration signal then the measurement accuracy is increased.…”