Evaluation method of statistical error in transit time measured with cross-correlation of two detector signals.
Akira ENDOU · Journal of Nuclear Science and Technology · 1983
In the transit time method for measuring flow velocity, the cross-correlation function of two detector signals is computed; the delay time which maximizes the function gives the transit time of the fluid between the detectors. The cross-correlation function is mathematically defined for an infinite observation time, however actually it is computed based on a finite length of time. Due to this approximation, the measured cross-correlation function has a statistical uncertainty, which induces a scattering on the measured transit time. In this paper, it is shown that the statistical error of the transit time may be expressed by using either the derivatives of correlation functions or the power spectral densities. The spectral expression has a merit of giving an intuitive understanding of the nature of the error and it can be seen that the error becomes smaller as the higher frequency components of the spectra increase. The error also becomes smaller when the coherence function has a larger value and/or the observation time extends for a longer period. A simplified evaluation method of the error is proposed using a trapezoidal approximation for the power spectra and this method is applied to the transit time measurement by electro- magnetic-flowmeters. The evaluated statistical error closely agreed with the measured scattering.