On the Combination of Random Matrix Theory With Measurements on a Single Structure

On the Combination of Random Matrix Theory With Measurements on a Single Structure

Igea, Felipe (University of Oxford)
Chatzis, Manolis N. (University of Oxford)
Cicirello, A. (TU Delft Mechanics and Physics of Structures)

2022

An approach is proposed for the evaluation of the probability density functions (PDFs) of the modal parameters for an ensemble of nominally identical structures when there is only access to a single structure and the dispersion parameter is known. The approach combines the Eigensystem realization algorithm on sets of dynamic data, with an explicit nonparametric probabilistic method. A single structure, either a mathematical model or a prototype, is used to obtain simulated data or measurements that are employed to build a discrete time state-space model description. The dispersion parameter is used to describe the uncertainty due to different sources such as the variability found in the population and the identification errors found in the noisy measurements from the experiments. With this approach, instead of propagating the uncertainties through the governing equations of the system, the distribution of the modal parameters of the whole ensemble is obtained by randomizing the matrices in the state-space model with an efficient procedure. The applicability of the approach is shown through the analysis of a two degrees-of-freedom mass-spring-damper system and a cantilever system. The results show that if the source of uncertainty is unknown and it is possible to specify an overall level of uncertainty, by having access to a single system's measurements, it is possible to evaluate the resulting PDFs on the modal parameters. It was also found that high values of the dispersion parameter may lead to nonphysical results such as negative damping ratios values.

http://resolver.tudelft.nl/uuid:991a8d19-cb0b-44cc-ac76-41398e712896

https://doi.org/10.1115/1.4054172

2023-07-01

2332-9017

ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 8 (4)

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© 2022 Felipe Igea, Manolis N. Chatzis, A. Cicirello