Coriolis flowmeter

Advantages of measuring with a Coriolis flowmeter:

• high accuracy of parameter measurements;
• work regardless of flow direction;
• straight sections of the pipeline before and after the flow meter are not required;
• reliable operation in the presence of vibration of the pipeline, when the temperature and pressure of the medium are changed (only if the flowmeter is mounted on rubber gaskets);
• long service life and ease of maintenance due to the absence of moving and wearing parts;
• measure the flow rate of high viscosity media;

Also, these devices are used to measure the flow of LPG .

Over the past 20 years, interest in mass Coriolis flowmeters has increased significantly [1]. Mass flow rate is obtained in a mass Coriolis flowmeter by measuring the phase difference of the signals from two sensors, the fluid density can be associated with the frequency of the signals [2]. Therefore, the frequency of the signal and the phase difference of the signals from the mass Coriolis flowmeter must be monitored with high accuracy and with a minimum delay. Under conditions of a two-phase (liquid / gas) flow, all signal parameters (amplitude, frequency, and phase) are subject to large and rapid changes, and the ability of tracking algorithms to monitor these changes with high accuracy and minimum delay is becoming an increasingly important task.

The Fourier transform is one of the most studied, universal and effective methods for studying signals [3,4]. This determines its continuous improvement and the emergence of methods that are closely related to it, but superior in some respects. For example, using the Hilbert transform [5], it is easy to implement amplitude and phase carrier demodulation, and PRISM [6] allows you to efficiently work with random signals represented by the sum of damped complex exponentials.

The transformations listed above can be attributed to nonparametric methods [3], which have a fundamental restriction on the frequency resolution associated with the observation time by the uncertainty relation: where and are the necessary frequency resolution and the observation time necessary to ensure it, respectively. This ratio imposes strict requirements on the duration of the observed section with high resolution requirements, which in turn degrades the dynamic characteristics of processing algorithms and makes it difficult to work with non-stationary signals.

The Hilbert-Huang transform [7] expands the possibility of working with non-stationary nonlinear signals, however, to date, it is based more on empirical conclusions, which makes it difficult to develop recommendations for its specific application.

One way to overcome the uncertainty relation is to switch to parametric signal processing methods, in which it is assumed that the signal consists of the sum of partial signals of a known shape (usually orthogonal in time or frequency), and only some signal parameters are unknown. For example, if a complex sinusoid is used as a partial signal, then the parameters are the complex amplitude, frequency of each component. Based on the principles of solving systems of independent equations, this makes it possible to reduce the number of samples of the signal to the number of unknown parameters, which can be orders of magnitude less than the number of samples necessary for use in the Fourier transform with the same resolution characteristics.

Perhaps the most famous methods of this class are algorithms based on regression processes and moving average processes [3]. Nevertheless, if the signal can be represented as a linear combination of exponential functions, the Prony method, proposed back in the late 18th century [8], is widely used. The main disadvantage of this method is the need for accurate knowledge of the number of exponential components included in the signal and a sufficiently strong sensitivity to additive noise [9]. The desire to overcome these shortcomings led to the emergence of one of the most effective methods of spectral analysis - the method of matrix beams (IMF) [10, 11 ^[1] ]. The number of exponential components is determined in the course of the method. In addition, studies show that the IMF has a significantly higher resistance to additive noise than the Prony method, and approaches in this parameter to the Rao-Cramer estimate [12].

In [13], methods for processing current signals from a Coriolis flowmeter to track the amplitude, frequency, and phase difference are considered and their characteristics are analyzed when modeling the conditions of a two-phase flow. These methods include Fourier transform, digital phase locked loop, digital correlation, adaptive notch filter, and Hilbert transform. In their next article [14], the authors described the complex bandpass filter algorithm and applied it to signal processing from a mass Coriolis flowmeter. To estimate the parameters of signals from a Coriolis flowmeter, the article [15 ^[2] ] also applies a modification of the classical matrix beam method for vector processes, which has shown better results compared to the Hilbert method and the classical matrix beam method.

• 1. Wang, T. Coriolis flowmeters: a review of developments over the past 20 years, and an assessment of the state of the art and likely future directions / T. Wang, R. Baker // Flow Meas. Instrum. 2014. - V. 40 No. 1. - P. 99–123.
• 2. Henry, M. Self-validating digital Coriolis mass flow meter / M. Henry // Comput. Control Eng. - 2000. - V. 11, No. 5. - P. 219–227.
• 3. Marple, SL Digital spectral analysis: with applications / SL Marple. - New Jersey: Prentice-Hall, 1987 .-- 492 p.
• 4. Sergienko, A.B. Digital signal processing / A.B. Sergienko. - St. Petersburg: Publishing House Peter, 2002 .-- 608 p.
• 5. Rabiner, LR Theory and application of Digital Signal Processing / LR Rabiner, B Gold - New Jersey: Prentice-Hall, 1975 .-- 762 p.
• 6. Henry, MP Prism Signal Processing for Sensor Condition Monitoring / MP Henry, O. Bushuev, O. Ibryaeva // 2017 IEEE 26th International Symposium on Industrial Electronics ISIE. - 2017. - V. 10, No. 2. - P. 224–276.
• 7. Huang, NE A review on Hilbert-Huang transform: Method and its applications to geophysical studies / NE Huang, Z. Wu. // Reviews of geophysics. - 2008. - V. 46, No. 2. - P. 1–23.
• 8. Prony, G. Essai experimental et analytique: sur les lois de la dilatabilite de fluides elastiques et sur celles de la force expansive de la vapeur de l'eau et de la vapeur de l'alkool, a differentes temperatures / G. Prony // JE Poly tech. - 1795. - V. 1, No. 2. - P. 24–76.
• 9. Kumeresan, R. Prony method for noisy data: Choosing the signal components and selecting the order in exponential signal models / R. Kumaresan, DW Tufts, LL Scharf // Proceedings of the IEEE. - 1984. - V. 72, No. 2. –P. 230-233.
• 10. Hua, Y. Matrix Pencil Method for Estimating Parameters of Exponentially Damped / Undamped Sinusoids in Noise / Y. Hua, TK Sarkar // IEEE Trans. Acoust Speech Signal Process. - 1990. - V. 38, No. 5. - P. 814–824.
• 11. O. Ibryaeva, D. Salov, "Matrix Pencil Method for Coriolis Mass Flow Meter Signal Processing in Two-Phase Flow Conditions", 2017 International conference on Industrial Engineering (ICIE) to appear. , pp. 4, 2017. ^[1]
• 12. Sarrazin, F. Comparison between Matrix Pencil and Prony methods applied on noisy antenna responses / F. Sarrazin, A. Sharaiha, P. Pouliguen // Loughborough Antenna and Propagation Conference Loughborough Antennas & Propagation Conference. - 2011 .-- P. 1 - 44.
• 13. Li, M. Signal Processing Methods for Coriolis Mass Flow Metering in Two-Phase Flow Conditions / M. Li, MP Henry // in 2016 IEEE International Conference on Industrial Technology (ICIT). - 2016. –V. 1, No. 1 - P. 1‑14.
• 14. Li, M. Complex Bandpass Filteringfor Coriolis Mass Flow Meter Signal Processing / M. Li, MP Henry // in 42nd IEEE Industrial Electronics Conference. - 2016. –V. 1, No. 1 - P. 133‑137.
• 15. Henry, M.P. The method of matrix beams for estimating the parameters of vector processes / M.P. Henry, O.L. Ibraeva, D.D. Salov, A.S. Semenov // Bulletin of SUSU. Series “Mathematical Modeling and Programming” - 2017 - V. 10, No. 4. - P. 92 - 105. ^[2]

• Coriolis flowmeters
• CORI-FLOW Coriolis Flow Meters