Combination of operational modal analysis algorithms to identify modal parameters of an actual centrifugal compressor

TL;DR

This paper introduces a statistical framework to fuse modal-parameter estimates from multiple Operational Modal Analysis (OMA) algorithms, yielding an approximate joint Gaussian distribution for parameters such as $\omega_d$ and $\zeta$ and enabling uncertainty quantification without full Bayesian computation. The approach partitions ambient vibration data into windows, applies several OMA methods (COV-SSI, DATA-SSI, MOBAR) to each window, and models the resulting estimates as Gaussian mixtures to obtain mean values and confidence ellipses. Applied to field data from a nine-impeller centrifugal compressor and benchmarked against stability verification testing (SVT) EMA results, the method delivers accurate modal parameters with quantified uncertainties at low computational cost, while accounting for both measurement and modeling uncertainties. The work demonstrates potential for improved rotordynamic design, model validation, and real-time health monitoring by providing fast, reliable modal estimates and interpretable uncertainty regions.

Abstract

The novelty of the current work is precisely to propose a statistical procedure to combine estimates of the modal parameters provided by any set of Operational Modal Analysis (OMA) algorithms so as to avoid preference for a particular one and also to derive an approximate joint probability distribution of the modal parameters, from which engineering statistics of interest such as mean value and variance are readily provided. The effectiveness of the proposed strategy is assessed considering measured data from an actual centrifugal compressor. The statistics obtained for both forward and backward modal parameters are finally compared against modal parameters identified during standard stability verification testing (SVT) of centrifugal compressors prior to shipment, using classical Experimental Modal Analysis (EMA) algorithms. The current work demonstrates that combination of OMA algorithms can provide quite accurate estimates for both the modal parameters and the associated uncertainties with low computational costs.

Figures (6)

• Figure 1: Proposed strategy: Raw time data is partitioned into time windows of length $T_a$ considering an overlapping $\Delta T$. Data from the $r$-th time window is provided as the input to the $j$-th OMA algorithm which in turn provides an estimate of modal parameters $\boldsymbol{\theta}^{(j,r)}$. The set of samples is enriched by restarting the whole process with different overlapping lengths $\Delta T$ to generate new samples. The whole set of samples is used to built a joint probability model.
• Figure 2: Compressor that recycles a mixture of components made predominantly of hydrogen gas.
• Figure 3: Illustrative sketch presenting the set of vibration and bearing temperature sensors of the compressor train. The symbol $T$ stands for temperature sensors, $X$, $Y$ stands for directions where displacements sensors monitoring radial displacement take place, $\phi$ stands for the phase measurements, $G/B$, $LS$, $HS$, $M$ and $C$ stands for gearbox, low speed shaft, high speed shaft, motor and compressor respectively.
• Figure 4: Full spectrum $\tilde{F}(\omega)$ computed with data $d_X(t)$ and $d_Y(t)$ measured at the Non Drive End during field operations at the maximum continuous speed (MCS). Spectrum number denotes the number of the realization for which the full spectrum was computed.
• Figure 5: Full spectrum $\tilde{F}(\omega)$ computed with data $d_X(t)$ and $d_Y(t)$ measured at the Drive End during field operations at the maximum continuous speed (MCS). Spectrum number denotes the number of the realization for which the full spectrum was computed.