Approximate representation of the statistics for extreme responses of single degree-of-freedom system excited by non-stationary processes

The objective of this study is to estimate the statistics of the maximum response of a structural system excited by a non-stationary process. To provide basic information for the design of structures, the response of a single degree-of-freedom (SDOF) system subjected to a non-stationary Gaussian white noise is considered. For this purpose, we first derive the probabilistic properties of the maximum values of a non-stationary and zero-mean white noise, whose standard deviation varies temporally under some limited conditions. Then, using the obtained properties, we propose a method to estimate the stochastic properties of the maximum response of a given SDOF system excited by a non-stationary white noise whose time-varying standard deviation is known. The validity of the obtained results is confirmed through Monte Carlo simulation.