Stochastic modeling of engineering dynamic excitations for stochastic dynamics of structures

The concepts of abstract function and random function for the description of stochastic processes are first revisited. Basic thought of physical stochastic processes is then delineated. In contrast to the traditional modeling, where the measured data are statistically analyzed to obtain second-order characteristics, e.g. covariance function or power spectral density, in the present framework the physical background/mechanism of stochastic dynamic excitations is first studied and used as a basis to construct a random function of basic random variables, of which the probability information is then identified via measured data. Modeling of fluctuating wind speed process via physical stochastic model is exemplified. Stochastic response analysis and reliability evaluation of a nonlinear structure by incorporating the physical stochastic model of wind excitation into the probability density evolution method are implemented. Investigation results validate the proposed approach.