A Martingale approach to the reliability of a structural system under nonstationary excitation

Abstract In this paper, an approach to reliability analysis is being proposed using the Martingale property of the response of the structure to nonstationary excitation. The dynamic equation being an Ito differential equation, the derived moments of the associated Fokker-Planck equation are expressed in simple forms. The Fokker-Planck equation is then solved to give the transition probability density function which characterizes the behavior of the structure. The reliability function is then obtained from the transition probability density function.