Largest absolute value statistics for the response of linear structures

A correct prediction of the largest absolute value of the dynamic response is a central topic in the reliability analysis of structures subjected to natural actions, such as earthquakes, winds and waves, which can be effectively modeled as random processes. Nevertheless, the exact statistics of the maximum absolute value have not been derived, even in the simplest case of a linear oscillator under normal stationary white noise; hence, a number of approximations can be found in the literature. In this paper, a censored Gumbel closure is proposed for the evaluation of the non-linear differential equations governing the statistical moments of the largest absolute value of the response of linear structures under stationary or nonstationary Gaussian processes. The principal characteristics of the proposed approach are: (i) the censored closure satisfies the natural constraint that the extreme absolute value of the response is always not less than the modulus of the response; (ii) the use of the Gumbel distribution for the closure improves the results in comparison with the Gaussian one.