PEER REVIEW
20
th
Australian International Aerospace Congress, 27-28 November 2023, Melbourne
ISBN number: 978-1-925627-66-4
Normal Paper
Enhanced multi-order probabilistic approach for rotation
speed estimation using the short-time Iterative Adaptive
Approach
Cédric Peeters
1
, Andreas Jakobsson
2
, Jérôme Antoni
3
, Jan Helsen
1
1
Department of Applied Mechanics, Vrije Universiteit Brussel, Brussels, Belgium
2
Center for Mathematical Sciences, Lund University, Sweden
3
Univ Lyon, INSA Lyon, LVA, Villeurbanne, France
Abstract
The multi-order probabilistic approach is a time-frequency-based signal processing method to
estimate the instantaneous angular speed of a rotating shaft using vibrations. It exploits the fact
that most rotating machines consist of multiple shafts and gears that produce strong,
deterministic vibrations. These periodic vibrations show up as families of harmonics in spectral
analysis. The multi-order probabilistic approach employs the short-time Fourier transform or
STFT to estimate the non-stationary instantaneous angular speed since it is a robust, non-
parametric time-frequency decomposition that does not suffer from cross-terms, performs well
at low signal-to-noise ratios, and has a low computational cost. Nowadays however, there are
new high-resolution non-parametric spectral estimators that have positioned themselves as
potential alternatives to the STFT. One promising alternative is the short-time Iterative
Adaptive Approach or ST-IAA which offers a higher resolution than the STFT in exchange for
an increased computational cost. This paper investigates the potential of the ST-IAA to enhance
the accuracy of the multi-order probabilistic approach since it allows to employ shorter time
windows while reducing sidelobes and leakage. The performance of the method is evaluated
on experimental vibration data measured on the gearbox of a civil aircraft engine. To properly
assess the accuracy of the ST-IAA-based multi-order probabilistic approach, it is compared to
several other state-of-the-art vibration-based speed estimation techniques. The results show that
the ST-IAA-based multi-order probabilistic approach can reliably outperform the conventional
STFT-based version.
Keywords: vibration signal processing, time-frequency analysis, instantaneous rotation speed
estimation, condition monitoring.
Introduction
Spectral analysis of one-dimensional, non-stationary, time-domain signals plays a vital role in
many signal processing methodologies. In the field of machine monitoring, spectral analysis of
such non-stationary signals is of particular interest to the research community due to the
presence of this type of signals in many industrial applications. A concrete example is the
inherent non-stationary nature of most rotating machines. In order to analyse measurement data
originating from a machine operating in non-stationary conditions, a commonly employed
approach is to visualize a time-frequency representation (TFR) of the data. This data can involve
measurements of the machine vibrations, currents, or acoustics. Visualizing the TFR of these
signals can be valuable for various reasons and has therefore been used for multiple different
purposes. In general, there has been ample research in the last few decades that tries to improve
existing TFR methods, resulting in many new techniques for TF decompositions [1,2,3,4,5,6].
