Application to Modal Updating

Bayesian Methods for Structural Dynamics and Civil Engineering 

Independent prior distributions for the parameters are taken as follows a Gaussian distribution for the natural frequencies with mean 0.5(2m - 1) Hz and a coefficient of variation 10% for the mth mode. Furthermore, the Rayleigh coefficients, the modal participation factor and the spectral intensity of the prediction error are assumed to be uniformly distributed over a sufficiently wide range to let the likelihood function determine their values. Note that the ranges of these distributions do not affect the model class selection results since they influence all modal models in the same way. Therefore, the computation of the Ockham factor and plausibility will exclude the prior PDF of these parameters but the one for the modal frequencies will still be included. 

The Bayesian spectral density approach in Chapter 3 is used for parametric identification. The spectral density estimator is utilized up to 8 Hz to include all the peaks so No, = 480. Table 6.2 shows the optimal modal frequencies for model classes with different number of modes. There is in general no difficulty in identifying the first five modes but it is not the 

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