Time Delay Study of Ultrasonic Gas Flowmeters Based on VMD–Hilbert Spectrum and Cross-Correlation

Abstract

The accuracy of ultrasonic flowmeter time delay measurement is directly affected by the processing method of the ultrasonic echo signal. This paper proposes a method for estimating the time delay of the ultrasonic gas flowmeter based on the Variational Mode Decomposition (VMD)–Hilbert Spectrum and Cross-Correlation (CC). The method improves the accuracy of the ultrasonic gas flowmeter by enhancing the quality of the echo signal. To denoise forward and reverse ultrasonic echo signals collected at various wind speeds, a Butterworth filter is initially used. The ultrasonic echo signals are then analyzed by Empirical Mode De-composition (EMD) and VMD analysis to obtain the Intrinsic Mode Function (IMF) containing distinct center frequencies, respectively. The Hilbert spectrum time–frequency diagram is used to evaluate the results of the VMD and EMD decompositions. It is found that the IMF decomposed by VMD has a better filtering performance and better anti-interference performance. Therefore, the IMF with a better effect is selected for signal reconstruction. The ultrasonic time delay is then calculated using the Cross-Correlation algorithm. The self-developed ultrasonic gas flowmeter was tested on the experimental platform of the gas flow standard devices using this signal processing method. The results show a maximum indication error of 0.84% within the flow range of 60–606 m3/h, with a repeatability of no more than 0.29%. These results meet the 1-level accuracy requirements as outlined in the national ultrasonic flowmeters calibration regulation JJG1030-2007.

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“…Throughout this step, the center frequency and bandwidth of each IMF are dynamically adjusted. Equation (22) is the expression of the IMF components [ 20 ]: where A k ( t ) is the instantaneous amplitude of IMF component; is its phase function; w k ( t ) is its instantaneous phase; and .…”

“…Throughout this step, the center frequency and bandwidth of each IMF are dynamically adjusted. Equation ( 22) is the expression of the IMF components [20]:…”