Simulation Study of the Application of Hilbert Transform in Two-phase Flow Parameters Measurements using Gamma-ray Absorption


two-phase flow
gamma ray absorption
random signals
time delay estimation
Hilbert Transform


Measuring of parameters of two-phase flows usually needs the contactless measuring techniques to be used together with advanced methods of signal processing. One of these techniques, which are employed for many years in measurements of liquid-gas, liquid-solids and gas-solid particles flows is a method of gamma-ray densitometry. Frequently in such measurements the mutually delayed stochastic signals are received from the scintillation detectors. For the time delay estimation the well-known cross-correlation method is usually used due to the random nature of the signals and presence of disturbances. This paper describes a proposition of use of Hilbert Transform to time delay estimation in radioisotope measurements of two-phase flow. It presents results of simulation study of the modified cross-correlation method, in which the Hilbert Transform of one measured signal is used. The simulations have been carried out for models of stochastic signals, corresponding to signals received in investigations of liquid-gas flow through horizontal pipeline, carried out with use of gamma-ray absorption technique. It has been stated that the described method provides better metrological properties than classical cross-correlation.



Falcone G., Hewitt G.F., Alimonti C. Multiphase flow metering: principles and applications, Elsevier, Amsterdam, 2009.

Johansen G.A., Jackson P. Radioisotope gauges for industrial process measurements. New York, John Wiley, 2004.

Roshani G. H., Nazemi E., Feghhi S. A. H., Setayeshi S. Flow regime identification and void fraction prediction in two-phase flows based on gamma ray attenuation. Measurement, 62 (2015), 25–32.

Nazemi E., Roshani G.H., Feghhi S.A.H., Setayeshi S, Eftekhari Zadeh E., Fatehi A. Optimization of a method for identifying the flow regime and measuring void fraction in a broad beam gamma-ray at-tenuation technique. Int. J. Hydrogen Energ., 41 (2016), 7438-7444.

Zych M., Hanus R., Vlasak P., Jaszczur M., Petryka L. Radiometric methods in the measurement of particle-laden flows. Powder Technol., 318 (2017), 491-500.

Roshani G.H., Nazemi E., Shama F., Imani M.A., Mohammadi S. Designing a simple radiometric sys-tem to predict void fraction percentage independent of flow pattern using radial basis function. Met-rol. Meas. Syst., 25(2) (2018), 347–358.

Zych M., Hanus R., Wilk B., Petryka L., Świsulski D. Comparison of noise reduction methods in radi-ometric correlation measurements of two-phase liquid-gas flows. Measurement, 129 (2018), 288–295.

Hanus R., Zych M., Kusy M., Jaszczur M., Petryka L. Identification of liquid-gas flow regime in a pipeline using gamma-ray absorption technique and computational intelligence methods. Flow Meas. Instrum., 60 (2018), 17-23.

Zhao Y., Qincheng B., Richa H. Recognition and measurement in the flow pattern and void fraction of gaseliquid two-phase flow in vertical upward pipes using the gamma densitometer. Appl. Therm. Eng., 60 (2013), 398-410.

Petryka L., Hanus R., Zych M., Śleziak M. Radioisotope measurements of two-phase flow. Przegl. Elektrotech., 86(5) (2010), 24-29, (in Polish).

Salgado C. M., Pereira C., Schirru R., Brandão L. E. B. Flow regime identification and volume fraction prediction in multiphase flows by means of gamma-ray attenuation and artificial neural networks. Prog. Nucl. Energy, 52 (2010), 555-562.

Zych M. An analysis and interpretation of the signals in gamma-absorption measurements of liquid–gas intermittent flow. Acta Geophys., 66 (2018), Art. ID 1435.

Beck M.S., Pląskowski A. Cross-correlation flowmeters. Their design and application. Adam Hilger, Bristol, 1987.

Bendat J.S., Piersol A.G. Random data - analysis and measurement procedures. (4th ed.) New York, John Wiley, 2010.

Tal B., Bencze A., Zoletnik S., Veres G., Por G. Cross-correlation based time delay estimation for turbulent flow velocity measurements: statistical considerations. Phys. Plasmas, 18 (2011), 122304.

Mosorov V. Phase spectrum method for time delay estimation using twin-plane electrical capacitance tomography. Electr. Letters, 42(11) (2006), 630-632.

Yang W.Q., Beck M.S. An intelligent cross correlator for pipeline flow velocity measurement. Flow Meas. Instrum., 8 (1998), 77-84.

Mosorov V. Flow pattern tracing for mass flow rate measurement in pneumatic conveying using twin plane electrical capacitance tomography. Part. Part. Syst. Char., 25(3) (2008), 259-265.

Mosorov V. A method of transit time measurement using twin plane electrical tomography. Meas. Sci. Technol., 17 (2006), 753-760.

Bendat J.S. The Hilbert Transform and applications to correlation measurements, Brüel&Kjær, BT0008-11, Naerum, Denmark, 1985.

Cabot R.C. A note on the application of the Hilbert transform to time delay estimation. IEEE Trans. Acoust., Speech, Signal Processing, 29 (1981), 607-609.

Hanus R. Estimating time delay of random signals using Hilbert Transform and analytic signal. Przegl. Elektrotech., 88(10a) (2012), 46-48, (in Polish).

Hanus R. Time delay estimation of random signals using cross-correlation with Hilbert Transform. Measurement, 146 (2019), 792-799.

Jacovitti G., Scarano G. Discrete time technique for time delay estimation. IEEE Transactions on Sig-nal Processing, 41(2) (1993), 525-533.

Hanus R., Kowalczyk A., Szlachta A., Chorzępa R. Application of conditional averaging to time delay estimation of random signals. Meas. Sci. Rev., 18(4) (2018), 130-137.

Hanus R. Accuracy comparison of some statistic methods of time delay measurements. Syst. Anal. Model. Sim., 40(2) (2001), 239-244.

Hanus R., Zych M. Simulation study of the application of Hilbert Transform in correlation measure-ments of liquid-gas flow using gamma-ray attenuation technique. 2019 8th International Conference on Systems and Control (ICSC), 23-25 Oct. 2019, Marrakesh, Morocco, 490-494.

Soo S.L. (ed). Instrumentation for fluid-particle flow. Noyes Publications, New Jersey 1999.

Velicković Z.S. Pavlović V.D. Complex analytic signals applied on time delay estimation. Acta Univ. HTS Nis, s. Phys. Chem. and Technol., 6 (2008), 11-28.

Shors S.M., Sahakian A.V., Sih H.J, Swiryn S. A method for determining high-resolution activation time delays in unipolar cardiac mapping. IEEE T. Bio-med. Eng., 43(12) (1996), 1192 - 1196.

Hanus R. Investigation of the correlation method of time delay estimation with Hilbert Transform of measuring signal. Przegl. Elektrotech., 88(10b) (2012), 39-41, (in Polish).

Hanus R. Application of the Hilbert Transform to measurements of liquid-gas flow using gamma ray densitometry. Int. J. Multiphas. Flow, 72 (2015), 210-217.

Svilainis L., Lukoseviciute K., Dumbrava V., Chaziachmetovas A. Subsample interpolation bias error in time of flight estimation by direct correlation in digital domain. Measurement, 46(10) (2013), 3950-3958.

Hanus R., Zych M., Petryka L., Świsulski D. Time delay estimation in two-phase flow investigation using the γ-ray attenuation technique. Math. Probl. Eng., (2014) Article ID 475735.

Guide to the expression of uncertainly in measurement. International Organisation for Standardisa-tion 1995.

Hanus R., Zych M., Petryka L., Hanus P. Application of Hilbert Transform to signal processing in radioisotope measurements of the liquid – solid particles flow in the vertical pipeline. In: XXI IMEKO World Congress Congress “Measurement in Research and Industry”, August 30 - September 4, 2015, Prague, Czech Republic. Full Papers Book, 1080-1083.