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New Numerical and Statistical Determination of Probes’ Arrangement in Turbo-machinery

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Abstract

Purpose

Blade tip timing (BTT) is a promising non-contact method for the measurements of blade tip displacement in turbo-machinery. Despite the advantages, this method offers, one of its drawbacks is the highly under-sampled data measured. The quality of these data depends on the position of the probes in the engine casing. This work aims to determine the placement of the probes for which the highest quality of data, hence the best accuracy of the vibration parameters are obtained.

Methods

Thus, the present work proposes a statistical BTT method based on the minimization of some statistical variables to determine the placement of the probes.

Results

This work presents a defined number of probes, which of the regular and irregular probe arrangement leads to the determination of vibration parameters with higher accuracy. It is found that mostly all the subsets with probes irregularly spaced are the ones giving a better accurate estimation of the amplitudes.

Conclusion

This work has proposed statistical methods of determination of the probes arrangement, based on the minimization of the RMSE in the case of synchronous vibrations and the combination of synchronous and asynchronous vibrations. In addition, we have shown statistically that in almost all the scenarios considered, the irregular probe placements are the ones for which the vibration parameters are obtained with the highest accuracy.

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Abbreviations

TOA:

Time of arrival

BTT:

Blade tip timing

RMSE:

Root-mean-square error

Std:

Standard deviation

bi:

Bias

\(N_{\text {reg}}\) :

Number of regular

\(N_{\text {irreg}}\) :

Number of irregular

\(N_{\text {up}}\) :

Number of upper half probes

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Funding

The European Regional Development Fund under Grant No. CZ.02.1.02 /0.0/0.0/15003/0000493, “CENDYNMAT - Centre of Excellence for Nonlinear Dynamics Behaviour of Advanced Materials in Engineering”; Clean Sky 2 under Grant EU H2020 BATISTA No. 862034 “Blade Tip Timing System Validator”; Academy of Sciences CR under Grant Strategy AV21, VP03: “Efficient energy conversion and storage, Vibrodiagnostics of rotating blades of rotary machines in power engineering”.

Author information

Author notes

  1. Eder Batista Tchawou Tchuisseu

    Present address: Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

  2. Eder Batista Tchawou Tchuisseu, Pavel Procházka, Mohammed Lamine Mekhalfia, Robert Hodbod’, Dušan Maturkanič, Pete Russhard, and Marek Brabec have contributed equally to this work.

Authors and Affiliations

  1. Institute of Thermomechanics of the Czech Academy of Sciences, Prague, Czech Republic

    Eder Batista Tchawou Tchuisseu, Pavel Procházka, Mohammed Lamine Mekhalfia, Robert Hodbod’ & Dušan Maturkanič

  2. Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic

    Marek Brabec

  3. EMTD Measurement Ltd. Derby, Great-Britain, England

    Pete Russhard

Authors
  1. Eder Batista Tchawou Tchuisseu
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  2. Pavel Procházka
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  7. Marek Brabec
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The authors of this article have equally contributed in the elaboration, edition, and review of the manuscript.

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Correspondence to Eder Batista Tchawou Tchuisseu.

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Tchawou Tchuisseu, E.B., Procházka, P., Mekhalfia, M.L. et al. New Numerical and Statistical Determination of Probes’ Arrangement in Turbo-machinery. J. Vib. Eng. Technol. 11, 2025–2035 (2023). https://doi.org/10.1007/s42417-022-00685-8

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