Sensitivity and Hessian matrix analysis of structural reliability for uniformly modulated random seismic response

Abstract

This paper presents a numerical method for calculation of the sensitivity and Hessian matrix of the time variant reliability of structures subjected to uniformly modulated evolutionary random seismic excitation. The first three spectral moments, their first and second derivatives are obtained using the auto PSD functions, their sensitivity and Hessian matrix information. The formulas of the first and second derivatives of reliability are derived by direct differentiation based on the reliability formula that assumes the threshold crossings to obey a two-state Markov process. The computational procedure is given in detail for the reliability, its first and second derivatives. Finally, the reliability, its sensitivity and Hessian matrix analysis of a planar frame subjected to the uniformly modulated evolutionary random earthquake ground motion has been studied to elucidate the proposed method. The accuracy and efficiency of the proposed method in this paper are discussed by comparison with the developed method.