Transient Perturbations of Gaussian White Noise Processes and Their Effects on the Extreme Response of Mechanical Oscillators

This paper presents a derivation for obtaining additive transient perturbations to Gaussian white noise (GWN) processes that induce any target level of maximum response on linear single‐degree‐of‐freedom oscillators over a time interval of length T. The metric to characterize the perturbation is the L 2 ‐norm, and the metric to characterize the extreme response is the probability of nonexceedance under the action of the GWN process. The paper also presents evidence that the proposed perturbation can also appear spontaneously in realizations of GWN that generate an extreme response in linear systems. This can be interpreted as a distinguishing characteristic of realizations of GWN that induce an extreme response in linear oscillators.