Discrete Time Series Synthesis of Randomly Excited Structural System Response

A set of digital computer techniques for the generation of second-order stationary time series for the experimental—numerical study of problems involving the response of structural systems under random excitation is described. A discrete time system whose output covariance is identically that of the regularly sampled observations of a white-noise excited continuous time dynamical system is synthesized to accomplish that objective. The dynamical system is assumed to be an n-degree-of-freedom (df) system represented by a set of ordinary differential equations. An economical scheme for the computation of the covariance function of the continuous system is first indicated. The 4n parameters of a mixed autoregressive-moving average time series scheme whose covariance function is that of the given continuous system are computed. 2n autoregressive time series parameters are determined by solving an appropriate set of Yule-Walker equations. These coefficients and the original covariances imply a set of algebraic quadratic equations that can be solved recursively for the remaining 2n moving average parameters. An algorithm to verify that this discrete time system does indeed duplicate the continuous system covariance function is also indicated. This latter technique is a simpler way to compute the mean-square responses of white-noise excited scalar output systems than was previously known. Examples of the synthesis of 2- and 10-df systems as well as the synthesis of a rigid body transfer function approximation to a rocket are worked.