Stochastic finite element model updating through Bayesian approach with unscented transform

Abstract

Finite element (FE) model updating is important and challenging. To address the issues of ill-conditioning and nonuniqueness, stochastic approaches have been developed for calibrating model parameters and associated uncertainties. Markov chain Monte Carlo (MCMC) methods have been widely used for stochastic model updating by providing a straightforward way to infer the posterior probability density function (PDF) using a sequence of random samples. However, the inherent nature relying on a large number of sampling points to approximate the posterior PDF of model parameters limits their application. In this paper, a Bayesian approach with unscented transform is investigated to perform stochastic model updating in a computational friendly way. Rather than using a large number of randomly chosen sampling points, the proposed approach selects a minimal set of sampling points to represent the PDF of model parameters. On the basis of the unscented transform, this approach effectively explores the distribution of measurements, from which model parameters and associated uncertainties are updated. Numerical simulation of a reinforced concrete beam is presented to show that the proposed approach can achieve similar model updating performance as the MCMC methods. The proposed Bayesian approach is further applied to update the FE model of a real-world cable-stayed bridge and provide quantitative assessment of the predication accuracy.

A Bayesian Structural Modal Updating Method Based on Sparse Grid and Ensemble Kalman Filter

“…Beck and Katafygiotis [27] built a more comprehensive and rigorous framework for Bayesian model updating and defned the concept of system identifcations. Recently, numerous studies of Bayesian model updating have been developed on analyzing both numerical examples and realworld applications [33][34][35]. Te schematic diagram of Bayesian model updating is shown in Figure 1.…”