Sensitivity and Hessian Matrix Analysis of Evolutionary PSD Functions for Nonstationary Random Seismic Responses

AbstractThis paper describes a numerical method for calculation of the sensitivity and Hessian matrix of the response evolutionary power spectral density (PSD) functions of structures subjected to uniformly modulated evolutionary random seismic excitation. The method is formulated based on the pseudoexcitation method and the Gauss precise time step integration method. The evolutionary nonstationary random response analysis is converted into step-by-step integration computations using the pseudoexcitation method. The formulas of the pseudoresponses and their first and second derivatives with respect to the structural design variables are derived based on the Gauss precise time step integration method. The evolutionary PSD functions, their sensitivity, and the Hessian matrix are calculated using the pseudoresponses and their first and second derivatives, respectively. Finally, the evolutionary PSD functions’ sensitivity and Hessian matrix analysis of a three-story, two-bay planar frame subjected to uniforml...

[1]  Liubin Yan,et al.  Response sensitivity and Hessian matrix analysis of planar frames subjected to earthquake excitation , 2009 .

[2]  W. Zhong,et al.  A Precise Time Step Integration Method , 1994 .

[3]  A. Kiureghian,et al.  Dynamic response sensitivity of inelastic structures , 1993 .

[4]  Liubin Yan,et al.  An optimal method for seismic drift design of concrete buildings using gradient and Hessian matrix calculations , 2010 .

[5]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[6]  Yu-Kweng Michael Lin,et al.  Probabilistic Structural Dynamics: Advanced Theory and Applications , 1967 .

[7]  Uri Kirsch,et al.  Efficient design sensitivities of structures subjected to dynamic loading , 2006 .

[8]  J. Szopa.  Sensitivity of stochastic systems to initial conditions , 1984 .

[9]  Jiahao Lin,et al.  Accurate and highly efficient algorithms for structural stationary/non-stationary random responses , 2001 .

[10]  Liubin Yan,et al.  A numerical method of calculating first and second derivatives of dynamic response based on Gauss precise time step integration method , 2010 .

[11]  Pierfrancesco Cacciola,et al.  A modal approach for the evaluation of the response sensitivity of structural systems subjected to non-stationary random processes , 2005 .

[12]  Subrata Chakraborty,et al.  Sensitivity evaluation in seismic reliability analysis of structures , 2004 .

[13]  S. Caddemi,et al.  Gaussian and non-Gaussian stochastic sensitivity analysis of discrete structural system , 2000 .