On the Combination of Random Matrix Theory with Measurements On a Single Structure

Abstract

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 non-parametric probabilistic method. A single structure, either a mathematical model or a prototype, are respectively 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 randomising the matrices in the state-space model with an efficient procedure. The applicability of the approach is shown through the analysis of a 2D0F mass-spring-damper system and a cantilever system. These 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 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 non-physical results such as negative damping ratios values.