Bayesian Updating with Approximated PDF Expansion

Let 0 denote the uncertain parameter vector for identification and it includes the following parameters  

The structural parameters that determine the model matrices M, C, and K. 

In the special case of modal updating, assume that only the lowest Nm modes contribute significantly to the response and only the modal parameters of these modes are to be identified. Then, the structural parameters are the modal frequencies modal damping ratios and the elements of the first mode shapes except those elements which are equal to unity for normalization purposes, m = 1,2,Nm- Thus, there are a total number of Nm No + 1) unknown structural modal parameters. 

The forcing parameters defining the spectral density matrix function Sg and the modulating function A. 

In the special case of modal identification, the first part of the forcing parameters are the elements of the upper right triangular part (diagonal inclusive) of the Nm x Nm submatrix of S fo of the modal forces (symmetry defines the lower triangular part). 

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