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Mathematical Problems in Engineering
Volume 2014, Article ID 475735, 10 pages
Research Article

Time Delay Estimation in Two-Phase Flow Investigation Using the γ-Ray Attenuation Technique

1Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, 35-959 Rzeszow, Poland
2Faculty of Geology, Geophysics and Environmental Protection, AGH University of Science and Technology, 30-059 Krakow, Poland
3Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, 30-059 Krakow, Poland
4Faculty of Electrical and Control Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland

Received 20 August 2014; Accepted 29 October 2014; Published 18 November 2014

Academic Editor: Qingling Zhang

Copyright © 2014 Robert Hanus et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Time delay estimation is an important research question having many applications in a range of technologies. Measurement of a two-phase flow in a pipeline or an open channel using radioisotopes is an example of such application. For instance, the determination of velocity of dispersed phase in that case is based on estimation of the time delay between two stochastic signals provided by scintillation probes. The proper analysis of such signals, usually in presence of noise, requires the use of advanced statistical signal processing. In this paper, the simulation studies of time delay estimation were carried out with the use of the following differential methods: average magnitude difference function, and average square difference function and proposed combined methods comprising the above-mentioned differential and cross-correlation functions are presented. Attached simulations have been carried out for models of stochastic signals corresponding to the signals obtained in gamma-ray absorption measurements of gas-liquid flow in a horizontal pipeline. The standard uncertainties of time delay estimations have been determined for each of the methods. Improved metrological properties have been stated in the combined methods in comparison with the classical cross-correlation procedure.