EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. 2001; 30:1103–1123 (DOI: 10.1002/eqe.53) Bayesian spectral density approach for modal updating using ambient data Lambros S. Katafygiotis *;† and Ka-Veng Yuen Department of Civil Engineering; Hong Kong University of Science and Technology; Clear Water Bay; Kowloon; Hong Kong SUMMARY The problem of identication 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 identied modal parameters is very important if one plans to proceed with the updating of a theoretical nite 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. Copyright ? 2001 John Wiley & Sons, Ltd. KEY WORDS: Bayesian; model updating; system identication; ambient vibrations; spectral density; structural health monitoring 1. INTRODUCTION The problem of identication of the modal parameters of a linear structural model using dynamic data has received much attention over the years because of its importance in model updating, response predictions, structural control and health monitoring. Many methodologies have been formulated, both in the time and frequency domain, for the case where the input excitation has been measured [1]. * Correspondence to: Lambros S. Katafygiotis, Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. † E-mail: lambros@ust.hk Contract=grant sponsor: Hong Kong Research Grant Council; contract=grant numbers: HKUST 639=95E, HKUST 6041=97E Received 29 June 1999 Revised 27 June 2000 Copyright ? 2001 John Wiley & Sons, Ltd. Accepted 24 October 2000