A reliability approximation for structures subjected to non-stationary random excitation

The main focus of this paper is to develop an approximate method for evaluating the reliability of structures subjected to non-stationary random excitation. Firstly, a commonly used exponential decay model is used for the reliability evaluation, in which the expected decay rates are obtained by VanMarcke’s formula. Then, normalization of structural responses is performed so that the expected decay rates can be formulated in terms of covariance of a structural response, its time derivative process and its Hilbert transformation at the same time. Finally, explicit solutions for above second-moment statistics of responses of single-degree-of-freedom (SDOF) systems subjected to modulated white noise excitation are given. The accuracy, efficiency and usage of the developed approximate method are demonstrated by the reliability analysis of SDOF systems subjected to two special types of uniformly modulated white noise excitations.