Operational Modal Analysis for Estimating the Dynamic Properties of a Stadium Structure during a Football Game

Abstract

During a football game, the ambient vibrations at the roof of a football stadium were recorded. A very large data set consisting of 4 hours of data, sampled at 80 Hz, is available. By a data reduction procedure, the complete data set could be analysed at once in a very short time. The data set was also split in shorter segments corresponding to certain events before, during and after the game to investigate the influence of varying operational conditions on the dynamic properties.As the structural vibrations were caused by unmeasurable wind and crowd excitation, Operational Modal Analysis has to be applied to find the dynamic characteristics of the structure. The new operational PolyMAX parameter estimation method is used and compared with Stochastic Subspace Identification. Stochastic Subspace Identification requires the correlations between the responses as primary data, whereas PolyMAX operates on spectra or half spectra (i.e. the Fourier transform of the positive time lags of the correlation functions). The main advantage of PolyMAX is that it yields extremely clear stabilisation diagrams, making an automation of the parameter identification process rather straightforward. This enables a continuous monitoring of the dynamic properties of a structure.

Automatic Tracking of the Modal Parameters of an Offshore Wind Turbine Drivetrain System

“…Estimating the auto and the cross-power spectra using the periodogram approach [17,18]; 3. Estimating the modal parameters of the drivetrain modes in the frequency band of interest using the polyreference Least-Squares Complex Frequency-domain (pLSCF) estimator [19][20][21]; 4. Automatic tracking of the modes of interest based on the Modal Assurance Criterion (MAC), frequency value, and damping ratio value.…”

“…An n th order right matrix-fraction model yields nN re f poles. For a displacement output quantity, the full power spectrum can be written as a function of the modal parameters (pole λ i ∈ C, modal operational reference factors V i ∈ C N re f ×1 , mode shapes ψ i ∈ C N o ×1 ) as [21,22]:…”

“…Estimating the modal parameters of the drivetrain modes in the frequency band of interest using the polyreference Least-Squares Complex Frequency-domain (pLSCF) estimator [19][20][21]; 4.…”

Full-scale modal wind turbine tests: comparing shaker excitation with wind excitation

“…OMA allows the investigator to collect modes that are relevant to the operation of the machine. A review of OMA methods can be found in [10] and some recent developments are discussed in [11]. The original application of OMA (although that name was not in use at that time) to wind turbines can be found in [12] [13].…”

“…Moreover, the use of an exponential window in the pre-processing stage is an excellent "de-noising" tool that could not be applied here. More details about the advantages of the use of half spectra (or correlograms) in comparison with the more classical spectra (or periodograms) can be found in [11]. In the near future, more extensive operational time-domain data will be acquired.…”