A D-norm cross-correlation method for particle velocity measurement through electrostatic sensing

The cross-correlation (CC) method is conventionally used for measuring the velocity of gas–solid flows using electrostatic sensors, wherein velocity measurement is transformed into a time-delay estimation problem. However, owing to the intricacies of signals in gas–solid flows, the cross-correlation function may exhibit multiple peaks, resulting in peak misjudgment and time-delay estimation bias. To address these issues, this paper proposes a D-norm cross-correlation (DCC) velocity measurement method and applies it to flow velocity measurements in pneumatic conveying. Such a technique leverages the sensitivity of D-norm to pulses, highlighting the pulse characteristics of measurement signals. This approach increases the accuracy of time-delay estimation for upstream and downstream signals, mitigating the issues caused by multi-peaks and fake peaks in the cross-correlation function. Compared to conventional CC, the DCC can eliminate the problem of multiple and fake peaks in cross-correlation functions more effectively, thereby increasing the reliability of velocity measurements.