Stochastic Galerkin model updating of randomly distributed parameters

Abstract

In this paper, we present a new stochastic model updating methodology to identify spatially varying material properties based on experimental data. This data is typically obtained from ambient or forced vibration measurements. For this purpose, a linear elastic property is modeled as a random field. Stochastic properties of the random field are quantified using an exponential covariance kernel. In order to combine the stochasticity with a Galerkin numerical model of a structure, the covariance kernel is discretized using the Karhunen-Loeve (KL) expansion. In the KL expansion, the covariance kernel is decomposed in the spectral domain by numerically solving a homogeneous Fredholm integral equation. For model updating, stochastic parameters are updated so that the Galerkin model provides dynamic properties matching with realizations that have been identified in experiments. In this paper, Gaussian realizations for varying properties have been employed for the corresponding reference model. This proposed method demonstrates its ability to identify the updating stochastic properties.

A novel approach for stochastic finite element model updating and parameter estimation

“…Moreover, Bayesian method is employed to update the stochastic part with limited observations. In addition, it can be applied to more complicated case if the stochastic field is considered 12,13 and this will be illustrated in a forthcoming paper.…”