Zahra Zhiyanpour - M.Sc. Student, Department of civil engineering, Sharif University of Technology, Tehran, Iran.
Ali Bakhshi - Associate Professor, Department of civil engineering, Sharif University of Technology, Tehran, Iran.
Mohammad Rahai - Formerly M.Sc. Student, Department of civil engineering, Sharif University of Technology, Tehran, Iran.

This paper focuses on an application of Bayes inference rule to evaluate the probability of damage in structures, using measured modal parameters and a set of possible damage states. For different combinations of the damageparameters and realizations of the random vari-ables, the modal parameters are calculated solving the basic eigenvalue problem in regards to associated uncertainties in density and elasticity. The results are used to calculate the stati-tics of the parameters given a specific damage state, the likelihood functions, as these are needed to calculate the probability of a given a set of measurements given a damage state. This paper discusses the effectiveness of the approach in identifying a particular damage state referred to as damage scenario. The discussion also considers the effect of error in the meas-urements, and the number of repeated measurements that are required to achieve a substantial confidence as to the presence of a particular damage state. Ranking of the estimated prob-abilities, after a set of measurements, offers guidance to the engineer as when and where to conduct a direct inspection of the structure.

Probabilistic Damage Detection; Damage States; Multivariate Likelihood Func-tion; Bayesian Updating.