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

• Published in: Computers & structures Vol. 182; pp. 325 - 336
• Main Authors: Yan, Wang-Ji, Wan, Hua-Ping, Ren, Wei-Xin
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.04.2017; Elsevier BV
• Subjects: Algebra; Algebraic method; Excitation; Gaussian process; Gaussian process model; Mathematical models; Normal distribution; Numerical analysis; Parameter sensitivity; Power spectrum density; Pseudo-Excitation Method; Sensitivity analysis; Spectral density function; Spectral sensitivity; Stochastic models; Studies; Algebraic method; Sensitivity analysis; Gaussian process model; Power spectrum density; Pseudo-Excitation Method
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2016.12.005

•This work deals with the local and global sensitivity of PSD for random responses analytically.•The work is conducted utilizing the Pseudo-Excitation Method (PEM).•Analytical formulae are derived on the basis of a direct algebraic method.•The analytical formulae are compact, devoid of modal truncation problem and efficient to program.•Global sensitivity analysis is implemented analytically by incorporating Gaussian process model. 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.