Bayesian spectral density approach for modal updating using ambient data

Abstract

SUMMARYThe problem of identiÿcation of the modal parameters of a structural model using measured ambient response time histories is addressed. A Bayesian spectral density approach (BSDA) for modal updating is presented which uses the statistical properties of a spectral density estimator to obtain not only the optimal values of the updated modal parameters but also their associated uncertainties by calculating the posterior joint probability distribution of these parameters. Calculation of the uncertainties of the identiÿed modal parameters is very important if one plans to proceed with the updating of a theoretical ÿnite element model based on modal estimates. It is found that the updated PDF of the modal parameters can be well approximated by a Gaussian distribution centred at the optimal parameters at which the posterior PDF is maximized. Examples using simulated data are presented to illustrate the proposed method.

Structural identification of Egnatia Odos bridges based on ambient and earthquake induced vibrations

“…(2001) using time domain stochastic subspace identification methods, in Beck et al (1994) using time domain least-squares methods based on correlation functions of the output time histories, in Verboten et al (2002), Gauberghe (2004) and Brincker et al (2001) using frequency domain least-squares methods based on full cross-power spectral densities (CPSD), and in Peeters and Van der Auweraer (2005) based on half spectra. Bayesian and maximum likelihood statistical methods have also been proposed, for example, in Katafygiotis and Yuen (2001), Guillaume et al (1999) and Verboten (2002). For the case of earthquake-induced vibrations, modal identification methods have also been developed either in time (Beck 1978;Beck and Jennings 1980) or in frequency (McVerry 1980) domains, 3 based on a minimization of the measure of fit between the time history or its Fourier transform of the acceleration responses estimated from the measurements and the corresponding ones predicted from a classically-damped modal model of the structure.…”

Bayesian Network Methods for Modeling and Reliability Assessment of Infrastructure Systems

“…A Bayesian framework is proposed in Yuen and Katafygiotis (2002) to explicitly treat uncertainties in sensor measurements and modeling assumptions to obtain distributions of the modal parameters, including the most probable values of the parameters and their uncertainties. Both Katafygiotis and Yuen (2001) and Au et al (2013) use data from ambient vibrations for modal identification to obtain updated distributions of the modal parameters. The system identification and damage detection problems described previously that are addressed in these studies are long-term monitoring problems, however.…”

Mode Shape Assembly for Ambient Modal Analysis Using a Two-Stage Bayesian Spectral Density Approach

“…Bayesian spectral density approach (BSDA) [4] proposed previously is novel since it can consider different kinds of uncertainties and provides a rigorous means for obtaining modal properties as well as their uncertainties which is useful for further risk assessment. However, there are some challenges related to its practical implementation: (1) BSDA requires solving a high-dimensional numerical optimization problem whose computational effort grows with the number of measured dofs and the number of modes to be identified.…”

“…Recent interest has arisen to calculate the uncertainties of identified modal parameters by using Bayesian approaches [1]. In the context of ambient modal analysis, a number of Bayesian approaches have been proposed [2,3,4]. These methods provide rigorous means for obtaining optimal modal properties as well as their uncertainties.…”