Analytical local and global sensitivity of power spectrum density functions for structures subject to stochastic excitation

A unified consideration of the computation of the local and global sensitivity of structural Power Spectral Density (PSD) functions for random responses is conducted utilizing the Pseudo-Excitation Method (PEM). Analytical formulae enabling the calculation of sensitivity of the first and the second order with respect to chosen parameters are derived on the basis of an efficient direct algebraic method. The analytical formulae are compact, devoid of modal truncation problem and efficient to program. Also, global sensitivity analysis is implemented analytically by incorporating Gaussian process model to provide an approximate relationship between PSD functions and the sensitive parameters. It is investigated how scattering of parameters could induce variation in response spectra from a more comprehensive viewpoint. The validity and efficiency of the presented methods are illustrated using a numerical example.