Bounds on Response Variability of Stochastic Systems

Abstract

A methodology to analytically and numerically evaluate the spectral distribution‐free upper bounds of the response variability of stochastic systems is developed. The structural systems examined consist of linearly elastic, statically determinate and indeterminate beams subjected to static loads. The analytical evaluation of these bounds is achieved by introducing the variability response function of the stochastic system. This is a function with many similarities to the frequency response function used in random vibration analysis. At the same time, the numerical evaluation of the bounds is carried out by means of the fast Monte Carlo simulation technique, which requires an extremely small sample size. In essence, the fast Monte Carlo simulation technique is a method to estimate numerically the variability response function, whose analytical evaluation is particularly cumbersome even for very simple stochastic systems. of equal importance is that this work provides not only insight into the underlying mechanisms controlling the response variability of a stochastic system, but also an analytical basis on which the analysis can be extended to trusses, frames, and two‐dimensional structures and eventually to nonlinear and/or dynamic problems.